CIHM 
Microfiche 
Series 
(Monographs) 


ICIVIH 

Collection  de 
microfiches 
(monographies) 


Canadian  Institute  for  Historical  IMicroreproductions  /  Institut  Canadian  de  microreproductions  historiques 


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Technical  and  Bibliographic  Notes  /  Notes  techniques  et  bibliographiques 


he  Institute  has  attempted  to  obtain  the  best  original 
}py  available  for  filming.  Features  of  this  copy  which 
ay  be  bibliographically  unique,  which  may  alter  any  of 
le  images  in  the  reproduction,  or  which  may 
gnificantly  change  the  usual  method  of  filming  are 
lecked  below. 

7l   Coloured  covers  / 
—I   Couverture  de  couleur 


~~]   Covers  damaged  / 


Couverture  endommag^e 


:   Covers  restored  and/or  laminated  / 
Couverture  restaur^e  et/ou  peliicui^e 

I   rover  title  missing  /  Le  titre  de  couverture  manque 

_J   Coloured  maps  /  Cartes  g6ographiques  en  couleur 

7~|   Coloured  ink  (i.e.  other  than  blue  or  black)  / 
—I   Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 

:   Coloured  plates  and/or  illustrations  / 
Planches  et/ou  illustrations  en  couleur 

:    Bound  with  other  material  / 
Reli^  avec  d'autres  documents 

"~|   Only  edition  available  / 
—    ?eule  edition  disponible 

~|    fight  binding  may  cause  shadows  or  distortion  along 
—I    interior  margin  /  La  reliure  serr6e  peut  causer  de 

I'ombre  ou  de  la  distorsion  le  long  de  la  marge 

int^rieure. 

"~|  Blank  leaves  added  during  restorations  may  appear 
— '  within  the  text.  Whenever  possible,  these  have  been 
omitted  from  filming  /  II  se  peut  que  certaines  pages 
blanches  ajout6es  lors  d'une  restauration 
apparaissent  dans  le  texte,  mais,  lorsque  cela  6tait 
possible,  ces  pages  n'ont  pas  et6  film^es. 


Additional  comments  / 
Commentaires  suppi^mentaires: 


L'Institut  a  microfilm^  le  meilleur  exemplaire  qu'il  lui  a 
6\6  possible  de  se  procurer.  Les  details  de  cet  exem- 
plaire qui  sont  peut-6tre  uniques  du  point  de  vue  bibli- 
ographique,  qui  peuvent  modifier  une  image  reproduite, 
ou  qui  peuvent  exiger  une  modification  dans  la  m^tho- 
de  nonnale  de  filmage  sont  indiquds  ci-dessous. 

Coloured  pages  /  Pages  de  couleur 

I I   Pages  damaged  /  Pages  endommag6es 


D 


Pages  restored  and/or  laminated  / 
Pages  restaurdes  et/ou  pellicul^es 


Q  Pages  discoloured,  stained  or  foxed  / 
Pages  d^color^es,  tachet^es  ou  piqu^es 

Pages  detached  /  Pages  d6tach6es 

I  y\  Showthrough  /  Transparence 

I      I   Quality  of  print  varies  / 


D 


Quality  in^gale  de  I'impression 

Includes  supplementary  material  / 
Comprend  du  materiel  suppl^mentaire 

Pages  wholly  or  partially  obscured  by  errata  slips, 
tissues,  etc.,  have  been  refilmed  to  ensure  the  best 
possible  image  /  Les  pages  totalement  ou 
partiellement  obscurcies  par  un  feuillet  d'errata,  une 
pelure,  etc.,  ont  ^t§  filmies  a  nouveau  de  fafon  k 
obtenir  la  meilleure  image  possible. 

Opposing  pages  with  varying  colouration  or 
discolourations  are  filmed  twice  to  ensure  the  best 
possible  image  /  Les  pages  s'opposant  ayant  des 
colorations  variables  ou  des  decolorations  sont 
filmees  deux  fois  afin  d'obtenir  la  meilleure  image 
possible. 


Various  pagings. 


lis  item  is  filmed  at  the  reduction  ratio  checked  below  / 

t  document  est  filme  au  taux  de  reduction  indiqui  ci-dessous. 


Ox 

14x 

18x 

22x 

26x 

30x 

1 

J 

1 

12x 


16x 


20x 


24x 


28x 


32x 


seflKJ 


:Wmsir^yiY^'mwi:.:^^z?m*k  ■. 


Th«  copy  filmed  h«r«  has  b««n  rsproducad  thanks 
to  tha  gonarosity  of: 

National  Library  of  Canada 


L'aKamplaira  film*  fut  raproduit  grica  *  la 
ginirosit*  da: 

Bibliothequa  nationale  du  Canad* 


Tha  imagas  appaaring  hara  ara  tha  bast  quality 
possibia  considaring  tha  condition  and  lagibility 
of  tha  original  copy  and  in  kaaping  with  tha 
filming  contract  spacif ications. 


Original  capias  in  printad  papar  covars  arm  filmad 
beginning  with  tha  front  covar  and  ending  on 
tha  last  paga  with  a  printed  or  illustrated  impree- 
sion,  or  the  back  cover  when  eppropriata.  All 
other  original  copies  are  filmed  beginning  on  tha 
first  paga  with  a  printed  or  illustrated  impres- 
sion, and  ending  on  the  last  page  with  a  printad 
or  illustrated  impression. 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  ^^  (meaning  "CON- 
TINUED"), or  tha  symbol  ▼  (meaning  "END"). 
whichever  appliaa. 


Las  imagas  suivantas  ont  *t*  reproduites  avec  le 
plus  grand  soin.  compta  tenu  de  la  condition  at 
da  la  nattet*  da  I'exemplaira  film*,  et  en 
conformity  avec  las  conditions  du  contrat  de 
filmaga. 

Lee  exemplaires  originaux  dont  la  eouverture  en 
papier  est  imprim4e  sont  filmea  en  commancant 
par  le  premier  plat  et  en  terminant  aoit  par  la 
derniAre  paga  qui  comporte  une  emprsinte 
d'impression  ou  d'iliustration,  soit  par  la  second 


Pli 


lion  l« 


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originaux  sont  filmis  en  commenpant  par  la 
premiere  page  qui  comporte  une  empreinte 
d'impression  ou  d'iliustration  et  en  terminant  par 
la  darniAre  paga  qui  comporte  une  telle 
amprainta. 

Un  das  symbolas  suivants  spparaitra  sur  la 
darniire  image  de  cheque  microfiche,  selon  le 
cas:  la  symbols  ^»-  signifie  "A  SUIVRE '.  le 
symbole  ▼  signifie  "FIN  ". 


Maps,  plates,  charts,  etc..  may  be  filmed  at 
different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  an  filmed 
beginning  in  the  upper  left  hend  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  ss 
required.  The  following  diagrams  illustrate  the 
method: 


Les  cartas,  planches,  tableaux,  etc..  peuvent  etre 
filmis  A  des  taux  da  reduction  diff*rents. 
Lorsque  le  document  est  trop  grand  pour  Atra 
reproduit  en  un  seul  cliche,  ii  est  film*  A  partir 
da  Tangle  supArieur  gauche,  de  gauche  A  droite. 
et  de  haut  an  bas.  an  prenant  le  nombre 
d'imagas  nteessaira.  Les  diagrammes  suivants 
illustrent  la  mAthoda. 


1  2  3 


1 

2 

3 

4 

5 

6 

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MICROCOPY    RESOLUTION   TEST   CHART 

(*NSI  and  ISO  TEST  CHART  No.  2) 


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_J  APPLIED  IIVMGE     I 

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k^^rrnu 


The  Radford  Architectural  Co. 


Riverside,  III.,  IJ.  S.  A. 


Chicago 


New  YorK 


"% 


Special! 


WITHOUT  extra  cost  to  our  readers  we 
have  added  to  this  vohime  the  perspective 
views  and  floor  plans  of  twenty-five  houses. 
The  complete  working  plans  and  specifications 
of  any  of  those  houses  will  be  mailed  the  same 
day  the  order  is  received. 

Send  all  ordors  to 
THE  RADFORD  ARCHITECTURAL  CO. 

IlIVKKSIDE,  ILL.,  U.  S.  A. 


M 


COPTRHiHIED.  190S 
BT  FREDERICK  J.  DRAKE  ft  CO. 


Ik   M-  BT   FKEPEKICK  d 


PREFACE 

"Good  wine,"  says  Shakespeare,  "needs  no  bush," 
which  of  course  means  that  when  a  thing  is  good  in 
itself,  praise  makes  it  no  better.  So  with  a  book,  if  it 
is  good,  it  needs  no  preface  to  make  it  better.  The 
author  of  this  book  flatters  himself  that  the  work  he 
has  done  on  it,  both  as  author  and  compiler,  is  good; 
therefore,  from  his  standpoint  a  preface  to  it  is  some- 
what a  work  of  supererogation.  His  opinion  regard- 
ing the  quality  of  the  book  may  be  questioned,  but 
after  forty  years'  experience  as  a  writer  of  books  for 
builders,  all  of  which  have  met  with  success,  and 
during  that  time  over  thirty  years  editor  of  one  of  the 
most  popular  building  journals  in  America,  he  feels  his 
opinion,  reinforced  as  it  is  by  thousands  of  builders 
and  woodworkers  throughout  the  country,  should  be 
entitled  to  some  weight.  Be  that  as  it  may,  however, 
this  little  book  is  sent  out  with  a  certainty  that  the 
one  and  a  half  million  of  men  and  boys  who  earn  their 
living  by  working  wood,  and  fashioning  it  for  useful 
or  ornamental  purposes,  will  appreciate  it,  because 
of  its  main  object,  which  is  to  lessen  their  labors  by 
placing  before  them  the  quickest  and  most  approved 
methods  of  construction. 

To  say  more  in  this  preface  is  unnecessary  and  a 
waste  of  time  for  both  reader  and  author. 

FRED  T.  HODGSON. 

COLLINGWOOD,    ONTARIO,  July,   I9O2, 


:  ,M 


I  CONTENTS 

3  PART  I 

I  carpenter's  geometry 

1  he  Circle g 

Tangents 1 1 

Degrees  ' ,'  14 

Circular  Ornamentation -8 

Finding  Centers 20 

Polygons 22 

Bisecting  Angles 28 

Octagons 30 

Straight  Line  Solutions 32 

Bisecting  Angles  with  Steel  Square 34 

Solutions  of  Problems  with  Steel  Square 38 

Ellipses,  Spirals  and  Other  Curves 41 

Describing  Elliptical  Curves 46 

Flexible  Radial  Guide 49 

Ovals 50 

Spirals 52 

Parabola  and  Its  Uses,  The 56 

Cycloidal  Curves 57 

PART  II 

PRACTICAL   EXAMPLES 

Segmental  Arches 61 

Flat  Arches " ' '.  62 

Horseshoe  Arches 62 

Lintel  Arches 63 

Elliptical  Arches 63 

Lancet  Arches " .  64 

Four  Centered  Arches 65 

Ogee  Arches 66 

Mouldings g^ 

Balusters  and  Turned-work 68 

Steel  Square,  Description  of 70 

Lumber  Rule "  71 

Brace  Rule 73 

b 


6  CONTENTS 

PAO» 

Table  of  Braces 75 

Octagon  Rule  on  Steel  Square 76 

Rafter  Rule  hy  Steel  Square 76 

Cutting  Bridging 78 

Dividing  Lines 79 

Laying  off  Pitches 81 

Cuts  and  Bevels  for  Rafters 83 

Bevels  for  Hips,  Jack  Rafters  and  Purlins 85 

Framing  Sills,  etc 8/ 

Trimming  Stairs,  Chimneys,  etc 89 

Framing  Corners,  etc 91 

Roofs  and  Roofing  Generally 06 

Lines  for  Hip  Roofs S 

Octagon  Hip  Roofs yg 

Lengths  of  Jack  Rafters 102 

Trussed  Roofs 103 

Sisser  Roofs 104 

Domical   Roofs 105 

Spires  and  Spire  Framing 108 

Triangular  Framing 109 

Timber  Scarfing  in  Various  Ways no 

Mortise  a.id  Tenon  in  Timber in 

Reinforcing  Timber n3 

Strapping  Timber 112 

Trussing  and  Strengthening  Timber n4 

PART  HI 

joi:;er's  work 

Laying  out  Kerfs nS 

Bending  Kerfed  Stuff ng 

Kerfing  for  an  Ellipse 120 

Kerfing  on  a  Rake 121 

Mitering  Circular  Mouldings 121 

Mitering  Circular  and  Straight  Mouldiujjs 122 

Mitering  Curved  Mouldings  in  Panels 122 

Laying  out  Curved  Hips 123 

Laying  out  Ogee  Hips  and  Rafters 124 

Laying  out  Curved  Hip?  and  Jack  Rafters 125 

Raking  Mouldings 126 

Raking  Mouldings  for  Pediments 128 

Laying  out  Faking  Mouldings  for  Circular  Pedi- 
ments   129 


CONTENTS  7 

rAGB 

Cutting  R?king  Mouldings  in  M'tcr-box 130 

Angle  Bits  at  Different  Angles 13 » 

Inside  Cornices  on  a  Rake 132 

Cluster  Columns ^33 

Bases  and  Capitals  of  Cluster  Columns 133 

Hoppers,  Regular *34 

Miter  Cuts  for  Hoppers 135 

Butt  Cuts  for  Hoppers l3o 

Housed  Hopper  Cuts ^3'* 

Corner  Blocks  for  Hoppers,  etc 139 

Corner  Blocks  for  Acute  Hoppers 140 

Miters  for  Square  Hoppers Mi 

Miters  for  Acute  Hoppers Ml 

Miters  for  Obtuse  Hoppers 142 

Compound  Hopper  Lmes 143 

Covering  a  Conical  Roof 149 

Gore  f-'r  Conical  Roof 15° 

Covering  Domical  Roofs 150 

Incli.ied  Domical  Roof 15* 

Circular  Door  Entrances 'S^ 

Bending  Block  for  Splayed  Heads I53 

Splayed  Soffits 154 

Gothic  Soffits 155 

Dovetailing ^S^ 

Common  Dovetailing 157 

Lapped  Dovetailing 158 

BFnd  Dovetailii.  ■ 159 

Splayed  Dovetai  ing 1 59 

Stairbui'ding 159 

Pitch-board  and  Strings loO 

Treads,  Risers  and  Strings 161 

Dog-legged  Stairs 102 

Table  of  Treads  and  Risers 163 

Winding  Stairs 163 

Open  String  Stairs 164 

Setting    '  -"il  and  Newel  Post 104 

Metho<         Forming  Step 165 

Brackettu  Steps 165 

Joiner's  Work  Generally 107 

Various  Styles  of  Stairs 168 

St}'les  of  Doors 169 

Description  of  Doors •   I/O 


■  '4: 


5  CONTENTS 

Window  Frames  and  Sections V?? 

Miscellaneous  Illustrations jli 

Description  of  Balloon  Framing...'.." .1, 

Sections  of  Bay  Window  Frames.. ,7^ 

Turned  Mouldings  and  Carved  Newels." ".   17^ 

Shingling,  Different  Methods ,7? 

Shingling  liip  Rafters ,^1 

Shingling  Valleys 'y 

Illustrations  of  Shingling /J 

Flashings  for  Valleys ".V;.'.". ". ; '. ". '. ; ; ;  • ' '  J7° 


BUILDERS 


PART  IV 

USEFUL   TABLES   AND   MEMO.RANDA   FOR 

Lumber  Measurement '^able. .  ,0, 

Strength  of  Materials Jo: 

Table  of  Superficial  or  Flat  Measure." ,8, 

Round  and  Equal-sided  Timber  Measure ...      "    " "  iS* 

Shingling '°'* 

Table  for  Estimating  Shingles . . . ." .ol 

Siding,  Flooring  and  Laths .0^ 

Excavations g'* 

Number  of  Nails  Required  in  Carpentry "v'-ork." ." "  igc 

Sizes  of  Boxes  for  Different  Measure-                    "  is? 

Masonry r^ 

Brick  Work ."..".""; J°S 

Slating :::::::;.": \li 

To  Compute  the  Number  of  Slates  of  a  Give"n  Size 

Required  per  Square ,00 

Approximate  Weight  of  Materials  for  Roofs .' ." .'  .* "   i8q 

Snow  and  Vvind  Loads "     o^ 

United  i  .ates  Weights  and  Measures." .".".' to? 

Land  Measure ,  rl 

Cubic  or  So'id  Measure. ..! .X? 

Linear  Measure ' .^. 

Square  Measure .- . 

Miscellaneous  Measures  and  Weights. .' inr 

Safe-bearing  Loads .^ 

Capacity  of  Cisterns    for   Each  "  "fen' Inches  '  in 
Depth 

Number  of  Nails  and  Tacks'per'Pound.". Jq, 

Wind  Pressure  on  Roofs .....  J^j 


:.3L. 


■1 


MODERN     CARPENTRY 


n 


1 


m 
3 


PART    I 

CARPENTER'S   GEOMETRY 

CHAPTER  I 

THE   CIRCLE 

While  it  is  not  absolutely  necessary  that,  to  become 
a  gO(^  '  mechanic,  a  man  must  need  be  a  good  scholar 
or  be  well  advanced  in  mathematics  or  geometry,  yet, 
if  a  man  be  proficient  in  these  sciences  they  will  be  a 
great  help  to  him  in  aiding  him  to  accomplish  his  work 
with  greater  speed  and  more  exactness  than  if  he  did 
not  know  anything  about  them.  This,  I  think,  all  will 
admit.  It  may  be  added,  however,  that  a  man,  the 
moment  he  begins  active  operations  in  any  of  the  con- 
structional trades,  commences,  without  knowing  it,  to 
learn  the  science  of  geometry  in  its  rudimentary 
stages.  He  wishes  to  square  over  a  board  and  employs 
a  steel  or  other  square  for  this  purpose,  and,  when  he 
ccratches  or  pencils  a  line  across  the  board,  using  the 
edge  or  the  tongue  of  the  square  as  a  guide,  while  the 
edge  of  th''  blade  is  against  the  edge  of  the  board  or 
parallel  with  it,  he  thus  solves  his  first  geometrical 
problem,  that  is,  he  makes  a  right  angle  with  the  edge 
of  the  board.  Thia  Is  one  step  forward  in  the  path  of 
geometrical  science. 

He  desires  to  describe  a  circle,  say  of  eight  inches 
diameter.     He  knows  instinctively  that  if  he  opens  his 

9 


nP 


10 


MODERN   CARPENTRY 


compasses  until  the  points  of  the  legs  are  four  inches 
apart,— or  making  the  radius  four  inches— he  can,  by 
keeping  one  point  fixed,  called  a  "center,"  describe  a 
circle  with  the  other  leg,  the  diameter  of  which  will 
be  eight  inches.  By  this  process  he  has  solved  a 
second  geometrical  problem,  or  at  least  he  has  solved 
It  so  far  that  it  suits  his  present  purposes.  These 
examples,  of  course,  do  not  convey  to  the  operator  the 
more  subtle  qualities  of  the  right  angle  or  the  circle, 
yet  they  serve,  in  a  practical  manner,  as  assistants  in 
every-day  work. 

When  a  man  becomes  a  good  workman,  it  go'.-s  with- 
out saying  that  he  has  also  become  possessor  of  a  fair 
amount  of  practical  geometrical  knowledge,  though  he 
may  not  be  aware  of  the  fact. 

The  workman  who  can  construct  a  roof,  hipped, 
gabled,  or  otherwise,  cutting  all  his  material  on  the 
ground,  has  attained  an  advanced  practical  knowledge 
of  geometry,  though  he  may  never  have  heard  of 
Euclid  or  opened  a  book  relating  to  the  science. 
Some  of  the  best  workmen  I  have  met  were  men  who 
knew  nothing  of  geometry  as  taught  in  the  books,  yet 
It  was  no  trouble  for  them  to  lay  out  a  circular  or 
elliDtical  stairway,  or  construct  a  rail  over  them,  a 
feai  that  requires  a  knowledge  of  geometry  of  a  high 
order  to  properly  accomplish. 

These  few  introductory  remarks  are  made  with  the 
hope  that  the  reader  of  this  little  volume  will  not  be 
disheartened  at  the  threshold  of  his  trade,  because  of 
his  lack  of  knowledge  in  any  branch  thereof.  To 
become  a  good  carpenter  or  a  good  joiner,  a  young 
man  must  begin  at  the  bottom,  and  first  learn  his 
A,  B,  C's,  and  the  difficuItiLs  that  beset  him  will  disap- 
pear one  after  another  as  his  lessons  are  learned.     It 


CARPENTERS    GEOMETRY 


II 


must  always  be  borne  in  mind,  however,  that  the  young 
fellow  who  enters  a  shop,  fully  equipped  with  a  knowl- 
edge of  general  mathematics  and  geometry,  is  in  a 
much  better  position  to  solve  the  work  problems  that 
crop  up  daily,  than  the  one  who  starts  work  without 
such  equipment.  If,  however,  the  latter  fellow  be  a 
boy  possessed  of  courage  and  perseverance,  there  is  no 


reason  why  he  should  not  "catch  up" — even  over- 
take— the  boy  with  the  initial  advantages,  for  what  is 
then  learned  will  be  more  apt  to  be  better  understood, 
and  more  readily  applied  to  the  requirements  of  his 
work.  To  assist  him  in  "catching  up"  with  his  more 
favored  shopmate,  I  propose  to  submit  for  his  benefit 
a  brief  description  and  explanation  of  what  may  be 
termed  "Carpenter's  Geometry,"  which  will  be  quite 


la 


MODERN  CARPENTR  " 


sufficient  ,f  he  learn  it  well,  to  enable  him  to  execute 
any  work  that  he  may  be  called  upon  to  perform  al 
Iw.I.  do  so  a- clearly  and  plainly  as  possible^nd  n 
as  few  words  as  the  instructions  can  beVamcd  so  as  o 
make  them  intelligible  to  the  student 

The  crcle  shown  in  Fig.  ,  is  drawn  from  th.^  center 
2.  as  shown,  and  may  be  said  to  be  a  plain  BaJie 
w.thm  a  continual  curved  line,  every  part  of  the  line 
bemg  equally  distant   from   the  center  ..      I     ^     he 

Tsir  d  c^mf'""^^^  ''  '''^-  ^'^  "-  ^^  ^^ 
Hne  l^t.^"^'^"'"f"^"^<-^  •«  called  the  diameter,  and  ^he 
1  ne  DE  .s  denommated    a  chord,   and    the  \re-i  on 

aZiT'^^t'  '7''  '■■-'  -^  ^'^  chord  i;^;::rd 

the  In  e".  tl  , h  "\'  ''''^'  ''  '  ""^  ^^^^^  '^on^ 

h.lf  L     .         .     ''  circumference  C.  and  is  always  one- 
half  the  length  of  the  diameter,  no  matter  what  Zt 
d.ametermaybe.     A  tangent  is  a  line  which  toJe 
the  crcumference  at  some  point  and  is  at  right  a  gle 
wuh  a  rad.al  l.„e  drawn  to  that  point  as  shown  Tc 

they  win '\f^'""',"""'"'^^  ^'^'^  ^^'fi--^'-^  as 
they  w,ll   be    frequently  used    when  explanations  of 

learner  should  memorize  both  the  terms  and  their  sig! 
n.ficat.ons  m  order  that  he  may  the  more  reld  fv 
understand  the  problems  submitted  for  solutLn  "^ 

t  frequently  happens  that  the  center  of  a  circle  is 
the   2^  '";  ""'  '^'  ^^""^  '■"  -^'-  to  compL 
Thecen  eVof  "'P'  ^'''  °'  ''''  circumference. 

BHC  I  i,  .  K ''  '""l''  T""  ^'  ^°""d  ^-  f-"«^vs:  let 
BTA  -,  ^H  ^  V'^'"'^  ^^  '^^  ^^-g'^-'nt  II;  and 
BJA  a  chord  enclosing  the  segment.  Bisect  or 
divide  m  equal  parts,  the  chord  BC  at  H  -, n  I 
down  from  this  point  to  D  Do  7hf  ^"^.^^^are 
chord    ATT>  '"^  ^ame  with  the 

-hord    AJL.   squaring    over    trom    J  to    D,  then  the 


CARPENTERS   GEOMETRY 


>S 


point  where  JD  and  HD  inteisect,  will  be  the  center 
of  the  circle. 

This  is  one  of  the  most  important  problems  for  the 
carpenter  in  the  whole  range  of  g' 'omctry  as  it  enables 
the  workman  to  local-;  any  center,  and  to  draw  curves 
he  could  not  othcrwlsr  describe  without  this  or  other 
similar  methods.  It  is  by  aid  of  this  problem  that 
through    any  three    points    not   in   a  straight   line,   a 


circle  can  be  drawn  that  will  pass  through  •    oh  of  .  ,€ 
three  points.     Its  usefulness  will  be  shown  further 
as  applied    to    laying    out    segmental    or    curved   t.-p 
window,  door  and  other  frames  and  sashes,   and  'he 
learner  should  thoroughly  master  this  problem  bcfor. 
stepping  further,  as  a  full  knowledge  of  it  will  assist 
him  very  materially  in  understanding  other  problems. 
The  circumference  of  every  circle  is  measured  by 
being  supposed  to  he  divided    into  360  equal   parts, 
called  degrees;   each  degree  containing  60  minutes,  a 


■I 


I ; 


14 


MODERN  CARPENTRY 


smaller  division  and  each  minute  into  60  steonds,  a 
still  imaller  division.  Degrees,  minutes,  and  seconds 
are  written  thus:  45°  15'  30",  which  is  read,  forty-five 
degrees,  fifteen  minutes,  and  thirty  seconds.  This,  I 
think,  will  be  quite  clear  to  the  reader.  Arcs  are  meas- 
ured by  the  number  of  degrees  which  they  contain:  thus, 
in  Fig.  3,  the  arc  AE,  which  contains  90°,  is  called  a 
quadrant,  or  the  quarter  of  a  circumference,  because 


^^i 

-/!• 

r^ 

u 

/a 

1      ^y-^- 

v^^\ 

/so* 


i 

V 


90°  is  one  quartei  cf  360°,  and  the  arc  ABC  whici*  <on- 
tains  180°,  is  a  semi-circumterence.  Every  c:;.g!e  is  also 
measured  by  degrees,  the  degrees  being  reckoned  on  an 
arc  included  between  its  sides;  described  from  the  ver- 
tex of  the  angle  as  a  center,  as  the  point  O,  Fig.  3; 
thus,  AOE  contains  90";  and  the  angle  BOD,  which  is 
half  a  right  angle,  is  called  an  angle  of  45"',  which  is 


>.v^i 


CARPENTER'S  GEOMETRY 


«5 


the  number  it  contains,  as  will  be  teen  by  counting 
off  the  spaces  as  shown  by  the  divisions  on  the  curved 
line  *D.  These  rules  hold  good,  no  matter  what  may 
be  the  diameter  of  the  circle.  If  large,  the  divisions 
are  large;  if  small,  the  divisions  are  small,  but  the 
manner  of  reckoning  is  always  the  same. 

One  of  the  qualities  of  the  circle  is,  that  when 
divided  in  two  by  a  diameter,  making  two  semicircles, 
any  chord  starting  at  the  extremity  of  such  a  diameter, 
as  at  A  or  B,  Fig.  4  -"'d  c.;tting  the  circumference  at 
any  point,  as  at  C.         >t  E,  a  line  drawn  from  this 


point  to  the  other  extremity  of  the  diameter,  will 
form  a  right  angle — or  be  square  with  the  first  chord, 
as  is  shown  by  the  dotted  lines  BCA,  BDA,  and  BEA. 
This  is  something  to  be  remembered,  as  the  problem 
will  be  found  useful  on  many  occasions. 

The  diagram  shown  at  Fig.  5  represents  a  hexagon 
within  a  circle.  This  is  obtained  by  stepping  around 
the  circumference,  with  the  radius  of  the  circle  on  the 
compasses,  six  times,  which  divides  the  circumference 
into  six  equal  parts;  then  draw  lines  to  each  point, 
which,  when  completed,  will  form  a  hexagon,  a  six- 
sided  figure.  By  drawirj  lines  from  the  points 
obtained  in  the  circumference  to  the  center,  we  get  a 


i6 


MODERN   CARPENTRY 


three-sided  figure,  which  is  called  an  equilateral  trl 
angle,  that  ,s,  a  triangle  having  all  its  srer:;t,t 


Iength;  as  AB,  ACand  BC.     ThedottOfllln.      U        U 

The   diagram   shown 

at  Fig.  6  illustrates  the 

method  of  trisecting  a 

right  angle  or  quadrant 

>nto  three  equal  parts. 

Let  A  be  a  center,  and 

with    the   same    radius 

intersect  at  E,  thus  the 
quadrant  or  right  anirle 
is  divided  into  three 
equal  parts. 


CARPENTER'S   GEOMETRY 


»7 


If  we  wish  to  get  the  length  of  a  straight  line  that 
shall  equal  the  circumference  of  a  circle  or  part  of 
circle  or  quadrant,  we  can  do  so  by  proceeding  as  fol- 
lows: Suppose  Fig.  7  to  represent  half  of  the  circle, 
as  at  ABC;  then  draw  the  chord  BC,  divide  it  at  P, 
join  it  at  A;  then  four  times  PA  is  equ-'  *o  the  cir- 
cumference of  a  circle  whose  diameter  is  xtC,  or  equal 
to  the  curve  CB. 

To  divide  the  quadrant  AB  into  any  number  of 
equal  parts,  say  thirteen,  we  simply  lay  on  a  rule  and 
make  the  distance  from  A  to  R  measure  three  and  one- 


fourth  mches,  which  are  thirteen  quarters  or  parts  on 
the  rule;  make  R2  equal  one-fourth  of  an  inch;  join 
KP;  draw  from  2  parallel  with  RP,  cutting  at  V;  now 
take  PV  in  the  dividers  and  set  off  from  A  on  the  circle 
thirteen  parts,  which  end  at  B,  each  part  being  equal 
to  PV,  and  the  problem  is  solved.  The  "stretchout" 
or  length  of  any  curved  line  in  the  circle  can  then  be 
obtained  by  breaking  it  into  segments  bv  chords.  a<= 
shown  at  BN. 

1  have  shown  in  Fig.  5,  how  to  construct  an  equi- 
lateral triangle  by  the  use  of  the  compasses.     I  give  at 


i8 


MODERN  CARPENTRY 


Fig  8  a  practical  example  of  how  this  figure,  in  con- 
nection with  circles,  may  be  employed  in  describing  a 
figure  known  as  the  trefoil,  a  figure  made  much  use  of 
in  the  construction  of  church  or  other  Gothic  work  and 
for  windows  and  carvings  on  doors  and  panelings. 
Each  corner  of  the  triangle,  as  ABC,  is  a  center  from 
which  are  described  the  curves  shown  within  the  outer 
circles.     The  latter  curves  are  struck  from  the  center 


O,  which  is  found  by  dividing  the  sides  of  the  equi- 
lateral triangle  and  squaring  down  until  the  lines  cross 
at  O.  The  joint  lines  shown  are  the  proper  ones  to 
be  made  use  of  by  the  carpenter  when  executing  his 
work.  The  construction  of  this  figure  is  quite  simple 
and  easy  to  understand,  so  that  any  one  knowing  how  to 
handle  a  rule  and  compass  should  be  able  to  construct 
it  after  a  few  minutes'  thought.  This  figure  is  the  key 
to  most  Gothic  ornamentation,  and  is  worth  mastering. 


CARPENTER'S   GEOMETRY 


»9 


There  is  another  method  of  finding  the  length  or 
"stretchout"  of  the  circumference  of  a  circle,  which  I 
show  herewith  at  Fig.  9.  Draw  the  semicircle  SZT, 
and  parallel  to  the  diameter  ST  draw  the  tangent  UZV; 
upon  S  and  T  as  centers,  with  ST  as  radius,  mark  the 
arcs  TR  and  SR;  from  R,  the  intersection  of  the  arcs, 
draw  RS  and  continue  to  U;  also  draw  RT,  and  con- 
tinue to  V;    then  the   line  VU  will   nearly  equal   in 


length  the  circumference  of  the  semicircle.  The 
length  of  any  portion  of  a  circle  may  be  found  as  fol- 
loA's:  Through  X  draw  RW,  then  VVU  will  be  the 
'  stretchout"  or  length  of  that  portion  of  the  circle 
marked  SX.  There  are  several  other  ways  of  deter- 
mining by  lines  a  near  approach  to  the  length  of  the 
circumference  or  a  portion  thereof;  but,  theoretically, 
the  exact  "stretchout"  of  a  circumference  has  not  been 
found   by  any  of   the   known   methods,   either  arith- 


30 


MODERN   CARPENTRY 


■■-^ 


No. ethod.  however.  th?t-;-:„^:,--^;;^ 
sample    so  convenient  and  so  accurate  as   the  a    th 
metical  one,  which  I  mve  hcrewifh      Tf  f     . 

the  diameter  of  a  circle  bvJi^"  H      ""'  ."""'^'P'^ 
Eive  the    lenath     f   Ik        ■     ^^  ^  ^'  *''"-'  Product  will 
I  ve  ine    length  of   the   c.rcumference,    very  nearlv 
These   figures   are    base  '    on   the   fact   fh./  , 

whose  diameter  is   i     «  tne   tact   that   a   circle 

With  ihe  exception 
of  the    formation   of 
mouldings,  and  orna- 
mentation where  the 
circle    and    its   parts 
take    a    prominent 
part,    1     have     sub- 
mitted nearly  all  con- 
cerning   the     figure, 
the  everyday  carpen- 
ter   will     be     called 

to  use Ti,A:rT  7  '•""  ""■ '  "■'"  "y  -^-i  ^t>'»v  ho„ 

lo  use  the  knowledge  now  given 

Before  leaving  the  subject,  however,  it  n  .  as 

well    to    show    how  a    curve,    havin,.  any  n  abt 

Tots'inTe'^   obtained-practicalV-if    bu.    th 
points  ,n  the  circumference  are  available;    as  referred 
to  in  the  explanation  given  of  Fifr    r      I  ,  f       '^^^^'^'^^^ 
there  are  three  points 'given  i^t^^-     ircur^  e^rj-n^r^: 

^an  bc^^^'T;  ^'^-  "•  ^'^"  ^h— ^-of  such  .IM 

by  strlht"r      '  "k"'''*"^  ^'^'  P°'"^^  ^«  -nd  BC 
by  straight  lines  as  shown,  and  by  dividing  these  lines 


^./^? 


CARPENTER'S  GEOMETRY 


»i 


^3 


and  squaring  down  as  shown  until  the  lin-f,  intersect  at 
O  ?.i  shown.  This  point  O  is  the  center  of  the  circle. 
It  frequently  happens  that  it  is  not  possible  to  find  a 
place  to  locate  a  center,  because  of  the  didmeter  being 
so  great,  as  in  segmental  windows  and  doc-s  of  large 
dimensions.      To  overcome    this  difficulty  a  method 


has  been  devised  by  which  the  curve  may  be  correctly 
drawn  by  nailing  three  wooden  strips  together  so  as  to 
form  a  triangle,  as  shown  in  Fig.  ii.  Suppose  NO  to 
be  the  chord  or  width  of  frame,  '  nd  QP  the  height  of 
segment,  measuring  from  the  springin';  lines  N  and  O; 
dsive  nails  or  pins  at  O  and  N,  keep  Lhe  triangle  close 
against  the  nails,  and  place  a  pencil  at  P,  then  slide 
the  triangle  against  the  pins  or  nails  whii.,  sliding,  and 
the  pencil  will  describe  the  necessary  curve.  The 
arms  of  the  triangle  should  be  several  inches  long'^-- 
than  the  line  NO,  so  that  when  the  pencil  P  arrives  at 
N  c    J,  the  arms  will  still  rest  against  the  pins. 


CHAPTER  II 

POLYGONS 

A  polygon  is  a  figure  that  is  bounded  by  any  number 

b    etnf   J'"''  '''''•'""  '^'"^  *h^  least'^that  can 
be  employed  ,n  surrounding  any  figure,  as  a  triangle. 

A  polygon  having  three  sides  is  called  a  trigon;  it  is 

st«  i    calf  "a  ?r''^"''  •*^'.^"^'^-     ^  P°'^^-  -i  ^oar 
sides  IS  call  a  tetragon;   it  is  also  called  a  square  and 

an    equilateral    rect- 
angle.     A    polygon 
of    five    sides    is    a 
pentagon.      A  poly- 
gon of  six  sides   is  a 
hexagon.      A    poly- 
gon of  seven  sides  is 
called    a    heptagon. 
_^  A  polygon  of  eight 
^.  .       ,  sides     is    called    an 

octagon.     A  polygon  of  nine  sides  is  called  a  nonagon 
A  polygon  of  ten  sides  is  called  a  decagon.    A  polygon 
of  eleven  sides  .s  called  an  undecagon.     And  a  poly- 
gon of  twelve  sides  is  called  a  dodecagon 

There  are  regular  and  irregular  polygons.  Those 
having  equal  sides  are  regular;  those  having  unequal 
sides  are  irregular.  Polygons  having  more  than  twelve 
sides  are  known  among  carpenters  by  being  denom- 
inated as  a  polygon  having  "so  many  sides."  as  a 
polygon  with  fourteen  sides,"  and  so  on. 

23 


CARPENTERS  GEOMETRY 


•J 


Polygons  are  often  made  ie  of  in  carpenter  work, 
particularly  in  the  formation  of  bay-windows,  oriels, 
towers,  spires,  and  similar  work;  particularly  is  this 
the  case  with  the  hexagon  and  the  octagon;  but  the 
most  used  is  the  equilateral  rectangle,  or  square; 
therefore  it  is  essential  that  the  carpenter  should 
know  considerable  regarding  these  figures,  both  as  to 
their  qualities  and  their  construction. 

The  polygon  having  the  least  lines  is  the  trigon, 
a  three-sided  figure.  This  is  constructed  as  follows: 
Let  CD,  Fig.  i,  be  any  given  line,  and  the  dis- 
tance CD  the  length  of  the  side  required.  Then  with 
one  leg  of  the  compass  on  D  as  a  center,  and  the  other 
on  C,  describe  the  arc 
shown  at  P.  Then  with 
C  as  a  center,  describe  an- 
other arc  at  P,  cutting  the 
fir-^t  arc.  From  this  point 
of  intersection  draw  the 
lines  PD  and  PC,  and  the 
figure  is  complete.  To 
get  the  miter  joint  of  this 
figure,  divide  one  sic", 
into  two  equal  parts,  and 

from  the  point  obtained  draw  a  line  through  opposite 
angle  as  shown  by  the  dotted  line,  and  this  line  will  be 
the  line  of  joint  a;  C,  or  foi  any  of  the  other  angles. 

The  square,  or  equilateral  rectangle,  Fig.  2,  may  be 
obtained  by  a  number  of  methods,  many  of  which  will 
suggest  themselves  to  the  reader.  I  give  <^'-  ethod 
that  may  prove  suggestive.  Suppose  tw(  .des  of  a 
square  are  given,  LHN,  the  other  sides  are  found  by 
taking  HL  as  radius,  and  with  LN  for  centers  make 
the  intersection  in  P,  draw  LP  and  NP,  which  com- 


f  I 


»4  MODERN  CARPENTRY 

The  do.«d  line  skoJLunl  mV     """'"  "" 


ure 
regular  miter, 
or  miter. 


leng<h  of  o^e  side  of  Zfi  ''"■=  ""''  '^P""''  "»  'o  .he 

line  i„.ofwo  X:f,'^''7rlT'''-'   '"""^  "'^ 
^^_L^  ^'^"^  B  square  up  a  line; 

'  "  *  "lake  BN  equal  to 

AB,    strike   an    arc 
3N  as  shown  by  the 
dotted  lines,  with  2 
3s   a  center   and  N 
as  a  radius,  cutting 
the  given  line  at  3. 
Take  A3  for  radius; 
from   A   and   B   as 
centers,    make    the 
intersection    in    D; 
from     D,     with     a 


CARPENTER'S  GEOMETRY 


'S 


radius  equal  to  AB,  strike  an  arc;  with  the  same  radius 
and  A  and  B  as  centers,  intersect  the  arc  in  EC.  By 
joining  these  points  the  pentagon  is  formed.  The  cut, 
or  angle  of  joints,  is  found  by  raising  a  line  from  2  and 
cutting  D,  as  shown  by  the  dotted  line. 

The  hexagon,  a  six-sided  figure  shown  at  Fig.  4.  |s 
one  of  the  simplest  to  construct.     A  quick  method  is 
described  in  Chapter  I,  when  dealing  with  circles,  but 
I  show  the  method  of  construction  in  order  to  be  cer- 
tain that  the  student  may  be  the  better  equipped  to 
deal  with  the  figure.     Take  the  length  of  one  side  of 
the  figure  on  compasses;   make  this  length  the  radius 
of  a  circle,   thus  describe  a   circle  as  shown.     Start 
from  any  point,  as  at  A,  and  step  around  the  circum- 
ference of  the  circle  with  the  radius  of  it,  and  the 
points     from 
which   to   draw 
the    sides    are 
found,    as    the 
radius  of  any  cir- 
cle   will    divide 
the  circum- 
ference    of     that 
circle    into    s  i  x 
equal  parts. 

This  figure  may 
be  drawn  without 
first  making  a  circle  if  necessary.  Set  off  two  equal 
parts,  ABC,  Fig.  5.  making  three  centers;  from  each, 
with  radius  AC,  make  the  intersection  as  shown, 
through  which  draw  straight  lines,  and  a  hexagon  is 
formed.  The  miter  joint  follows  either  of  the  straight 
lines  passing  through  the  center,  the  bev  '  indicating 
the  proper  angle. 


» 


aC 


Ai'ODERN  CARPENTRY 


in 


The    construction    of    a    henf3,r«« 
%ure  ™ay  be  .cc„.p,i,h:,    ,  fof„™  ."VeVAnt''' 
6,  be  a  if  ven  I-"        ^nr^  *u    j-     ""°^*-    ^-et  AB,  F  £. 

this  point,  thei    take  AR  f  .         '  '"J"'*''*^  "P  ^rom 

•nters'ect  the  line  fl^^  ^T  "':i'"'  "  ^^  ^  -"^".• 
A  as  center,  draw  the  curve  2  ,  ..""^'  "^'"'  ^"^ 
radius,  and  from  2  as  .  .^  '  ^'   ''''^"   *^'*^  KL  as 

draw  fron  it  to^!  TuninTaT'^-r "  ^^^  ^^  "  ^^ 
draw  from  A;  make  AD  Lual  Bv  •  7^''^  P°'"^ 
draw  from  3  parallel  with  AD  l^'  'T"  ^^  '"^  «I^' 
L.  cutting  at  C-  Join  it  and  A-  d  ;..  t"  ^  ^'^^^^^'^ 

'  '"^^-  'rem  3  parallel 
with  AC;  make 
3H  equal  AB. 
and  CE  equal 
ND;  join  ED; 
draw    from    H 

parallel  v/ith3C, 
cutting  at  F, 
join  this  line 
and  E,  which 
completes  t  h  e 
heptagon.  It  is 
not  often  this 
%ure  is  used  in 

though  I  have  sometimes  emploved  •  '  "■  P  ^  "  ^  --y  • 
bay  windows  and  dormer.  ^.  '"  '^instructing 
HF.   FE.   and  ED       Th    '  "7  ''\'^"^  "■^"'  3" 

-veswellinaconservXo    oThe^smH  ^'T   '"' 
It  IS  proper  th  t   fh„       -^""^  o^ner  similar  place. 

construe' th'fi'ure   as  .r:'"  ''"""''  """  ^"w  to 


«■ 


i 


CARPENTER'S  GEOMETRY 


«7 


tious  young  carpenter,  who  desires  to  become,  not  only 
a  good  workman,  but  a  good  draftsman  as  well. 

The  octagon  or  eight-sided  figure  claims  rank  next 
to  the  square  and  circle,  in  point  of  usefulness  to  the 
general  carpenter,  owing  partly  to  its  symmetry  of 
form,  and  its  simplicity  of  construction.  There  are  a 
great  number  of  methods  of  constructing  this  figure, 
but  I  will  give  only  a  few  of  the  simplest,  and  the  ones 
most  likely  to  be  readily  understood  by  the  ordinary 
workman. 

One  of  the  simplest  methods  of  forming  an  octagon 
is  shown  at  Fig.  7, 
where  the  corners  of 
the  square  are  used  as 
centers,  and  to  the  cen- 
ter A  of  the  square  for 
radius.  Parts  of  a  cir- 
cle are  then  drawn  and 
continued  until  the 
boundary  lines  are  cut. 
At  the  points  found 
draw  diagonal  lines 
across  the  corner  as 
shown,    and   the   figure 

will  be  a  complete  octagon,   having  all   its  sides  of 
equal  length. 

The  method  of  obtaining  the  joint  cut  or  miter  for 
an  octagon  is  shown  at  Fig.  8,  where  the  angle  ABC, 
is  divided  into  two  equal  angles  by  the  following 
process:  From  B,  with  any  radius,  strike  an  arc,  giving 
A  and  C  as  centers,  from  which,  with  any  radius,  make 
an  intersection,  as  shown,  .Tnd  through  it  from  B,  draw 
a  line,  and  the  proper  angle  for  the  cut  is  obtained,  the 
dotted  line  being  t'^e  angle  sought.     By  this  method 


•»  MODERN  CARPENTRY 

's  a  very  useful  prob- 
'em,    as    it   is  often 
called    into    requisi- 
tion   for    cutting 
mouldings  in  panels 
and     other     work, 
where  the  angles  are 
not     so-are,     as     in 
stair        ndrils     and 
raking  wainscot. 

-ta^^yvhen  the  length  of  one  of 'Lrr^.r 
as  AB,  F.g.  9,  square  up  the  two  lines.  AN,  BF.  then 


d'aw  th!  ''  '''^'"'  -^'"^   ^   ""^    ^   ^^   «"ters.    and 
draw  the  arcs,    cutting   the   two   lines   at   C  and  J; 


I 


CARPENTERS  GEOMETRY 


»9 


draw  from  AB,  through  CJ,  and  again  from  A  draw 
parallel  with  HJ;  then  draw  from  B  parallel  with 
AC;  make  BV  and  CF  equal  AB;  join  EV;  make 
CF  equal  CA;  square  over  FN;  join  FE;  draw  NP 
parallel  with  AC,  then  join  PR,  and  the  figure  is 
complete. 


As  the  sides  of  all  regular  octagons  are  at  an  angle 
of  45'"  with  each  other,  it  follows  that  an  octagon  may 
be  readily  constructed  by  making  use  of  a  set  square 
having  its  third  side  to  correspond  with  an  angle  of 
45°,  for  by  extending  the  line  AB,  and  laying  the  set 
square  on  the  line  with  one  point  at  B,  as  shown  in 
Fig.  10,  the  line  BV,  Fig.  9,  can  be  drawn,  and  when 
made  the  same  length  as  BV,  the  process  can  be 
repeated  to  VE;  and  so  on  until  all  the  points  have 
been  connected. 

Suppose  we  have  a  square  stic'.c  of  timber  12  x  12 
inches,  and  any  length,  and  we  wish  to  make  it  an  octa- 
gon; we  will  first  be  obliged  to  find  the  gauge  points 
so  as  to  mark  the  stick,  to  snap  a  chalk  line  on  it  so  as 
to  te!!  how  much  of  the  corners  must  be  removed  in 
order  to  give  to  the  stick  eight  sides  of  equal  width. 
We  do  this  as  follows:     Make  a  drawing  the  size  of  a 


'^^s 
'^'W^ 


'   ^^ 


J»  MODERN  CARPENTRY 

section  ot  the  timber,  that  is.  twelve  inches  square, 
then  draw  a  line  from  corner  to  corner  as  AB  Fig  ii 
and  make  AC  equal  in  length  o  A  D,  which 'is  twelve 
inches;  square  over  from  C  o  K;  set  yo.  gauge  to 
BK.  and  run  your  hnes  to  th  v  ,  juge.  ,.n<^  remove  the 
corners  off  to  lines,  and  the  s  !  •;:  vili  thea  be  an  octa- 
gon having  eight  equal  sides. 
There  are  a  number  of  other  methods  of  finding  the 


Ii 


• 


gauge  points,  some  of  which  I  may  describe  further  on 
but  I  think  I  have  dwelt  long  enough  on  polygons  to 
enable  the  reader  to  lay  off  all  the  examples  given. 
The  polygons  not  described  are  so  seldom  made  use 
of  in  carpentry,  that  no  authority  that  I  am  aware  of 
describes  them  when  writing  for  the  practical  work- 
man; though  in  nearly  all  works  on  theoretical  geom- 


aii?ii^5^^f3&c»gp.>^;t?ii.v«4^  :^ 


CARPENTER'S  GEOMETRY  31 

etry  the  figures  are  given  with  all  their  qualities.  If 
the  solution  of  any  of  the  problems  offered  in  this 
work  requires  a  description  and  explanation  of  poly- 
gons with  a  greater  number  of  sides  than  eight,  such 
explanation  will  be  given. 


I 


'i 


& 


I 


CHAPTER  III 

SOME   STRAIGHT   LINE   SOLUTIONS 

The  greatest  number  of  difficult  problems  in  carpen- 
Tn^llTT''^  of  solution  by  ?he  use  of  strl^'t 
i'nes  and  a  proper  application  of  the  steel  square,  and 

JT  in  this  chapter  I  will 

endeavor  to  show  the 

reader  how  some  of 

the  problems  may  be 

jr-     y       (  solved,   though   it  is 

^  ^-       I  not  intended  to  offer 


a  treatise  on  the 
subject  of  the  utility 
of  the  steel  square, 
as  that  subject  has 
been    treated    at 

works,  and  another  and  exnaustlj^^o!;;::::^-; 
preparat.on;  but  it  is  thought  no  work  on  arp^nt  y 
can  be  complete  without,  at  least,  showing  some  of  the 
solutions  that  may  be  accomplished  by  the  p7ope    use 

tTo::t''''  ■■""^""^^"-  ^"^  ^^''-•"  '-5:^-  - 

us  to  make  a  perpendicular  line  on  any  given  straiL^h' 

oiro::^'tt^'rK ''p^^  ^  -r--  ^''^  ^^  ^^^^^^^ 

and  r.'l.    p      -^    '      '^-  '•  ^"  '^"^  ^'■^•^'"  straight   line, 
and  make  F  any  point  in  the  .sn„an.  or  nerncndi-„'. 

1-e  required.      From  F  with  a,^  radius,  ^trt^i^ 

12 


j:^i^mimm^mg^M^^ 


CARPENTER'S  GEOMETRY 


33 


I 


cutting  in  JK;  with  these  points  as  centers,  and  any 
radius  greater  than  half  JK,  make  intersection  as 
shown,  and  from  this  point  draw  a  line  to  F,  and  this 
line  is  the  perpendicular  required.  Foundations,  and 
other  works  on  a  large  scale  are  often  "squared"  or 
laid  out  by  this  method,  or  by  another,  which  I  will 
submit  later. 

In  a  previous  illustration  I  showed  how  to  bisect  an 
angle  by  using  the  compasses  and  straight  lines,  so  as 
to  obtain  the  proper  joints  or  miters  for  the  angles.    At 
Fig.  2, 1  show  how  this  may  be  done  by  the  aid  of  the  steel 
square     alone, 
as  follows:  The 
angle    is    ob- 
tuse, and  may 
be   that  of   an 
octagon   or 
pentagon      o  r 
other  polygon. 
Mark  any  two 
points   on    the 
angle,  as  DN, 
equally  distant  from  the  point  of  angle  L;   apply  the 
steel  square  as  shown,  keeping  the  distance  EM  and 
ED  the  same,  then  a  line  running  through  the  angle  L 
and  the  point  of  the  square  E  will  be  the  line  sought. 
To  bisect  an  acute  angle  by  the  same  method,  pro- 
ceed as  follows:     Mark  any  two  points  AC,    Fig   3, 
equally  distant   from   B;    apply  the  steel   square   as 
shown,  keeping  its  sides  on  AC;  then  the  distance  on 
each  side  of  the  square  being  equal  from  the  corner 
gives  it  for  a  point,  through  which  draw  a  line  from  B, 
and  the   angle   is   divided.      Both  angles  shown   are 
divided  by  the  same  method,  making  the  intersection 


i 


(I 


34 


MODL/    I  CARPENTRY 


i>S  '■ 


in  P  the  center  of  the  trianeJe     Th^  ,«  •     .l- 
considered  l„^,u  -iu.iontio  L'^e"^'"  J^r^s^' 
"  ^  and   C    equal 

from  the  point 
B>"    also    an 
equal  distance 
from  the  point 
or   toe   of  the 
square    to   the 
points  of  con- 
tact C  and  A 
on    the    boun- 
dary lines. 
A  repetition 
method  of  bisectiniT  an«i«.        j  of    the    same 

shown  at  Fig  4     The  o!l?;  "     • ""  °'''^  ^^"ditions.  is 
S-  4.     1  he  process  is  just  the  same,  and  the 


iXuoiTre^es:!';.'''^  --•---'-'.- 


CARPENTER'S    GEOMETRY 


iS 


To  get  a  correct  miter  cut,  or,  in  other  words,  an 
anple  of  45°,  on  a  board,  make  either  cf  the  points  A 
or  C,  Fig.  5,  the  starting  point  for  the  miter,  on  the 
edge  of  the 
board,  then  ap- 
ply the  square 
as  shown,  keep- 
ing the  figure 
12"  at  A  or  C, 
as  the  case  may 
be,  with  the  fig- 
ure 12"  on  the 
other  blade  of  the  square  on  the  edge  of  the  board  as 
shown;  then  the  slopes  on  the  edge  of  the  square  from 
A  to  B  and  C  to  B,  will  form  angles  of  45°  with  the 
base  line  AC.  This  problem  is  useful  from  many 
points  of  view,  and  will  often  suggest  itself  to  the 
workman  in  his  daily  labor. 

To  construct  a  figure  showing  on  one  sid  ,>  an  angle 
of  30"  and  on  the  other  an  angle  of  60°,  by  the  use  of 


the  steel  square,  we  go  to  work  as  follows:  Mark  on  the 
edge  of  a  board  two  equal  spaces  as  AB,  BC,  Fig.  6, 
apply  the  square,  keeping  its  blade  on  AC  and  making 


\\ 


36 


MODERN   CARPENTRY 


h 


AD  equal  AB;  then  the  angles  30°  and  60°  a'^ 
formed  as  shown.  If  we  make  a  templet  cut  exactly 
as  shown  in  Fig.  5,  also  a  templet  cut  as  shown  in 
this  last  figure,  and  these  templets  are  made  of  some 
hard  wood,  we  get  a  pair  of  set  sqi  .res  for  drawing 
puri  OSes,  by  which  a  large  number  of  geometrical 
problems  and  drawing  kinks  may  be  wrought  out. 

The  diameter  of  any  circle  within  the  range  of  the 
steel  square  may  be  determi.ied  by  the  instrument  as 
follows:  The  corner  of  the  square  touching  any  part 
of  the  circumference  A,  Fig.  7,  and  the  blade  cutting 
in   points   C,  B,  gives  the  diameter  of  the  circle  as 


i 


shown.  Another  application  of  this  principle  is,  that 
the  diameter  of  a  circle  being  known,  the  square  may 
be  employed  to  describe  the  circumference.  Suppose 
CB  to  be  the  known  diameter;  then  put  in  two  nails 
as  shown,  one  at  B  and  the  other  at  C,  apply  the 
square,  keeping  its  edges  firmly  against  the  nails,  con- 
tinually sliding  it  around,  then  the  point  of  the  square 
A  wi'l  describe  half  the  circumference.     Apply  the 


I 


CARPENTER'S    GEOMETRY 


S7 


square  to  the  other  side  of  the  nails,  and  repeat  the 
process,  when  the  whole  circle  will  be  described.  This 
problem  may  be  appl-ed  to  the  solution  of  many  others 
of  a  similar  nature. 

At  Fig.  8,  I  show  how  an  equilateral  triangle  may 
be  obtained  by  the  use  of  a  square.     Draw  the  line 


DC;  take  12  on  the  blade  and  7  on  the  tongue;  mark 
on  the  tongue  for  one  side  of  the  figure.  Make  the  dis- 
tance from  D  to  A  equal  to  the  desired  length  of  one  side 
of  the  figure.  Reverse  the  square,  placing  it  as  shown  by 
the  dotted  lines  in  the  sketch,  bringing  7  of  the  tongue 
against  the  point  A.  Scribe  along  the  tongue,  pro- 
ducing the  line  until  it  intersects  the  first  line  drawn 
in  the  point  E,  then  AEB  will  be  an  equilateral  tri- 
angle. A  method  of  describing  a  hexagon  by  the 
square,  is  shown  at  Fig.  9,  which  is  quite  simple. 
Draw  the  line  GH;  lay  off  the  required  length  of  one 
side  on  this  line,  as  DE.  Place  the  square  as  before, 
with  12  of  the  blade  and  7  of  the  tongue  against  the 
line  GH;  placing  7  of  the  tongue  against  the  point  D, 
scribe  along  the  tongue  for  the  side  DC.  Place  the 
square  as  shown  by  the  dotted  lines;  bringing  7  of  the 
tongue  against  the  point  E,  scribe  the  side  EF.     Con- 


:i:  i 


1 


iSb 


i9W**ii 


ki 


jl  MODERN  CARPENTRY 

tinue  in  this  way  until  the  other  half  of  the  figure  is 
dravn.     All  is  shown  by  FAHC. 

Ine  manner  of  biscctiuff  angles  has  been  shown  in 
Figs.  2,  3  and  4  of  the  present  chapter,  so  that  it  is 
not  :>^cessary  to  repeat  the  process  at  this  time. 

The  method  of  describing  an  octagon  by  using 
the  square,  ir  shown  at    Fig.  10.       Lay  off    a   square 


section  with  any  length  of  sides,  as  AB.     Bisect  this 
side  and    place    the    s(]uare    as    shown    on    the    side 

AB,  with  the  length 
bisected  on  the  blade 
and  tongue;  then 
the  tongue  cuts  the 
side  at  the  point  to 
gauge  for  the  piece 
to  be  removed.  To 
find  the  size  of 
square  required  for 
an  octagonal  prism, 
when  the  side  is 
given:  Let  CD  equal 
the  given  side;  place 
the    square     on    the 


CARPENTER'S  GEOMETRY 


39 


line  of  the  side,  with  one-half  of  the  side  on  the  blade 
and  tongue;  then  the  tongue  cuts  the  line  at  the  point 
B,  which  determines  the  size  of  the  square,  and  the 
piece  to  be  removed. 
A  near  approxima- 
tion to  the  length  or 
stretch-out  of  a  cir- 
cumference of  a  cir- 
cle may  be  obtained 
by  the  aid  of  the 
steel  square  and  a 
straight  line,  as  fol- 
lows: Take  three 
diameters  of  the 
circle  and  measure  up  the  side  of  the  blade  of  the 
sfjuare,  as  shown  at  Fig.  1 1,  and  fifteen-sixteenths  of 
one  diameter  on  the  tongue.      From  these  two  points 


^.f^ 


24  U 

ihllllllll 


j^.l.i.i.i.i.T.l.i.i.i.M- 


I  DlAMETEfl* 


draw  a  diagonal,  aud  the  length  of  this  diagonal  will 
be  the  length  or  stretch-out  of  the  circumference  nearly. 
If  it  is  desired  to  divide  a  board  or  other  substance 
into  any  given  number  of  equal  parts,  without  going 
through  the  process  of  calculation,  it  may  readily  be 
done  by  the  aid  of  the  square  or  even  a  pocket  rule. 
AC,  BD,  ^i"   A2,  be  the  width  of  the  board  or 


I 


F 


^glweryVt^^f 


-■T-i^".' 


4« 


MODERN  CARPENTRY 


I 


other  material,  and  this  width  is  seven  and  one-quarter 
inches,  and  we  wish  to  divide  it  into  eight  equal 
parts.  Lay  on  the  board  diagonally,  witi.  furthermost 
point  of  the  square  fair  with  one  edge,  and  the  mark 
8  on  the  square  on  the  other  edge;  then  prick  off  the 
inches,  I,  2,  3,  4,  5,  6  and  7  as  shown,  and  these  points 
will  be  the  gauge  points  from  which  to  draw  the 
parallel  lines.  These  lines,  of  course,  will  be  some- 
thing less  than  one  inch  apart. 

If  the  board  should  be  more  than  eight  inch*^  i  wide, 
then  a  greater  length  of  the  square  may  be  jsed,  as 
for  instance,  if  the  board  is  ten  inches  wide,  and  we 
wish  to  divide  it  into  eight  equal  parts,  we  simply 
make  use  of  the  figure  12  on  the  square  instead  of  8, 
and  prick  off  the  spaces  every  one  and  a  half  inches 
on  the  square.  If  the  board  is  more  than  12  inches 
wide,  and  we  require  the  same  number  of  divisions:  we 
make  use  of  figure  16  on  the  square,  and  prick  off  at 
every  two  inches.  Any  other  divisions  of  the  board 
may  be  obtained  in  a  like  manner,  varying  only  the 
use  of  the  figures,  on  the  square  to  get  the  number 
of  divisions  required. 

As  a  number  of  problems  in  connection  with  actual 
work,  will  be  wrought  out  on  similar  lines  to  the  fore- 
going, further  on  in  this  book,  I  will  close  this  chapter 
in  order  to  give  as  much  space  as  possible  in  describ- 
ing the  ellipse  and  the  higher  curves. 


_  ■-<u^./. 


CHAPTER    IV 

ELLIPSES,    SPIRALS,    AND   OTHER    CURVES 

The  ellipse,  next  to  the  circle,  is  th  curve  the  car- 
penter  will  be  confro.  ted  with  more  than  any  other, 
and  while  it  is  not  intended  to  discuss  all,  or  even  a 
major  part,  of  the  properties  and  characteristics  of 
this  curve,  I  will  endeavor  to  lay  before  the  reader 
all  in  connection  with  it  that  he  may  be  called  upon 

to  deal  with. 

According  to  geometricians,  an  ellipse  is  a  conic 
section  formed  by  cutting  a  cone  through  the  curved 
surface,  neither  parallel  to  the  base  nor  making  a 
subcontrary  section,  so  that  the  ellipse  like  the  circle 
is  a  curve  that  returns  within  itself,  and  completely 
encloses  a  space.  One  of  the  principal  and  useful 
properties  of  the  ellipse  is,  that  the  rectangle  under 
t^-e  two  segments  of  a  diameter  is  as  the  square  of  the 
ordinate.  In  the  circle,  the  same  ratio  obtains,  but 
the  rectangle  under  the  two  segments  of  the  diameter 
becomes  equal  to  the  square  of  the  ordinate. 

It  is  not  necessary  that  we  enter  into  a  learned 
description  of  the  relations  of  the  ellipse  to  the  cone 
and  the  cylinder,  as  the  ordinary  carpenter  may  never 
have  any  practical  use  of  such  knowledge,  though,  if 
he  have  time  and  inclination,  such  knowledge  would 
avail  him  mu  :h  and  tend  to  broaden  his  tdcas^ 
Suffice  for  us  to  show  the  various  methods  by  which 
this  curve  may  be  obtained,  and  a  few  of  its  applica- 
tions to  actual  work. 

One  of  the  simplest  and  most  correct  methods  ot 
describing  an  ellipse,  is  by  the  aid  of  two  pins,  a  string 

4» 


11. 


<^' 


'^n^'-n' 


'^W^ 


t^r''"'':i  yj 


1^ 


Si 


4«  MODERN   CARPENTRY 

and  a  lead-pencil,  as  shown  at  Fig.  i.  Lot  FR  he  the 
major  or  lor.gist  ;ixis,  or  iliamet.r,  and  DC  the  minor 
or  Bhortcr  axis  or  diam-tcr,  and  E  and  K  the  two  foci. 


These  two  points  are  obtained  by  takiiifj  the  half  of 
the  major  axis  AH  or  FA,  on  the  compasses,  ar.d. 
standing  one  point  at  D,  cut  the  points  \\  and  K  on  the 
line  FB,  and  at  these  points  insert  the  pins  at  E  an!  K 
as  shown.  Take  a  string  a^  shown  i.y  the  dotted  lines 
and  tie  to  the  pins  at  K,  then  stand  the  pencil  at  C 
and  run  the  string  round  it  and  carry  the  string  to  the 
pin  E,  holding  it  tight  and  winding  it  once  or  twice 
around  the  pin,  and  then  holding  the  string  with  the 
finger  Run  the  pencil  around,  keeping  the  loop  of 
the  string  on  the  pencil  and  it  will  guide  the  latter  in 
the  formation  of  the  curve  as  shown.  When  one-half 
of  the  ellipse  is  formed,  the  string  nay  be  used  for  tlu 
other  half,  commencing  the  curve  at  F  or  B,  as  the 
case  may  be.  This  is  commonly  called  "a  gardener's 
oval,"  because  gardeners  make  use  of  it  for  forming 
ornamental  beds  for  flowers,  or  in  makmg  curves  for 


CARPENTER'S    GEOMETRY 


43 


FCg.2. 


walks,  etc..  etc.  This  method  of  forminp  the  curve, 
is  l-asi-ii  on  the  well-known  property  of  the  ellipse 
that  the  siim  of  any  two  lines  drawn  from  the  foci  to 
their  circumference 
is  the  same.  K^^  ^  ^ 

Another  m  e  t  h  od 
of  projecting  an 
ellipse  is  shown  at 
Fij,'.  2,  hy  iisinj,'  a 
trammel.  This  is  an 
instrument  consist- 
ing of  two  principal 
parts,  the   fixed    part 

in  the  form  of  a  cross  as  CD,  AB,  and  the  movable 
trac(  '  ilG.  The  fixed  piece  is  made  of  two  triangular 
bars  or  pieces  of  wood  of  eijual  thickness,  joined 
together  so  as  to  be  in  the  same  plane.  On  one  side 
of  the  frame  when  made,  is  a  groove  forming  a  right- 
angled  cross;  the  groove  is  shown  in  the  section  at  E. 
In  this  groove,  two  studs  are  fitted  to  slide  easily,  the 
studs  having  a  section  same  as  shown  at  F  These  stu  Is 
are  to  carry  the  tracer  and  guide  it  on  proper  lin-  '.. 
The  tracer  may  have  a  sliding  stud  on  the  end  to  carry 
a  lead-pencil,  or  it  may  have  a  number  of  small  holes 
passed  through  it  as  shown  in  the  cut,  to  carry  the 
pencil.  To  draw  an  ellipse  with  this  instrument,  we 
measure  off  half  the  distance  of  the  major  axis  from 
the  pencil  to  the  stud  G,  and  half  the  minor  axis  from 
the  pencil  point  to  the  stud  II,  then  swing  the  tracer 
round,  and  the  pencil  will  describe  the  ellipse  required 
The  sUuls  have  little  projections  on  their  tops,  that  fit 
easily  into  the  holes  in  the  tracer,  but  this  may  be 
done  away  w.^h,  and  two  brad  awls  or  pins  may  be 
thrust  through  the  tracer  and  into  the  studs,  and  then 


44 


MODERN   CARPENTRY 


'4'- 


proceed   with   the  work.      With   this    instrument  an 
ellipse  may  easily  be  described. 

Another  method,  based  on  the  trammel  principle,  is 
shown  at  Figs.  3  and  4,  where  the  steel  square  is  substi- 
tuted for  the  instru- 
^  ment  shown  in  Fig.  2. 

Draw   the   line  AB, 
bisecting  it  at  right 
Ib  angles,    draw    CD. 
Set  off    these    lines 


ituiUUiUiUMUuuuiuuuiu: 


the  required  dimen- 
sions of  the  ellipse  to 
be  drawn.  Place 
an  ordinary  square  as 
shown.  Lay  the  straightedge  lengthwise  of  the  figure, 
as  shown  in  Fig.  3,  and  putting  a  pin  at  E  against  the 
square,  place  the  pencil  at  F,  at  a  point  corresponding 
with  the  one  of  the  figure.  Next  place  the  straight- 
edge, as  shown  in 
Fig.  4,  crosswise 
of  the  figure,  and 
bring  the  pencil  F 
to  a  point  cor- 
responding to  one 
side  of  the  figure, 
and  set  a  pin  at  G. 
By  keeping  the 
two  pins  E  and  G 
against  the  square, 
and  moving  the  straightedge  so  as  to  carry  the  pencil 
from  side  to  side,  one-quarter  of  the  figure  will  be 
struck.  By  placing  the  square  in  the  same  relative 
position  in  each  of  the  other  three-quarters,  the  other 
parts  may  be  struck. 


CARPENTER'S  GEOMETRY 


45 


A  method,— and  one  that  is  very  useful  for  many 
purposes,— of    drawing  an    ellipse  approximately,   is 
shown  in  Fig.  5.     It  is  convenient  and  maybe  applied 
to  hundreds  of  purposes,  some  of  which  will  be  illus- 
trated  as   we   proceed. 
To  apply  this  method, 
work  as  follows:     First 
lay   off    the    length   of 
the   required   figure,  as 
shown  by  AB,   Fig.  5, 
and  the  width  as  shown 
by  CD.      Construct    a 
parallelogram  that  shall 
have   its  sides  tangent 
to  the  figure  at  the  points  of  its  length  and  width,  all 
as  shown  by  EFGH.     Subdivide  one-half  of  the  end 
of  the  parallelogram  into  any  convenient  number  of 
equal  parts,  as  shown  at  AE,  and  one-half  of  its  side 
in  the  same  manner,  as  shown  by  ED.     Connect  these 
two  sets  of  points  by  intersecting  lines  in  the  manner 
shown  in  the  engraving.      Repeat  the  operation  for 
each  of  the  other  corners  of  the  parallelogram.     A 
line  traced  through  the  inner  set  of  intersections  will 
be  a  very  close  approximation  to  an  ellipse. 

There  are  a  number  of  ways  of  describing  figures  that 
approximate  ellipses  by  using  the  compasses,  some  of 
them  being  a  near  approach  to  a  true  ellipse,  and  it  is 
well  that  the  workman  should  acquaint  himself  with 
the  methods  of  their  construction.  It  is  only  neces- 
sary that  a  few  examples  be  given  in  this  work,  as  a 
knowledge  of  these  shown  will  lead  the  way  to  the 
construction  of  others  when  required.  The  method 
exhibited  in  Fig.  6  is,  perhaps,  the  most  useful  of  any 
employed  by  workmen,  than  all  other  methods  com- 


46 


MODERN   CARPENTRY 


bined.  To  describe  it,  lay  off  the  length  CD,  and  at 
right  angles  to  it  and  bisecting  it  lay  off  the  width  AB. 
On  the  larger  diameter  lay  off  a  space  equal  to  the 
shorter  diameter  or  width,  as  shown  by  DE.     Divide 

the  remainder  of  the 
length  or  larger  diameter 
EC  into  three  equal  parts; 
with  two  of  these  parts 
as  a  radius,  and  R  as  a 
center,  strike  the  circle 
GSFT.  Then,  with  F  as 
a  center  and  FG  as  radius, 
and  G  as  center  and  GF 
as  radius,  strike  the  arcs  as 
shown,  intersecilrg  each  other  and  cutting  the  line 
drawn  through  the  shorter  diameter  at  O  and  P  respec- 
tively. From  O,  through  the  points  G  and  F,  draw 
OL  and  OM,  and  likewise  from  P  through  the  same 
points  draw  PK  and  PN.  With  O  as  center  and  OA 
as  radius,  strike  the 
arc  LM,  and  with  P 
as  center  and  with 
like  radius,  or  PB 
which  is  the  same, 
strike  the  arc  KN. 
With  F  and  G  as 
centers,  and  with  FD 
and    CG  which  are  _,.  „j^ 

the  same,  for  radii,  -^^-^      ^ 

strike  the  arcs  NM  and  KL  respectively,  thus  com- 
pleting the  figure.  Another  method  in  which  the  centers 
for  the  longer  arc  are  outside  the  curve  lines,  is  shown 
at  Fig.  7.  Let  AB  be  the  length  and  CD  the  breadth; 
join   BD  through   the  center  of  the  line  EB,  and  at 


CARPENTER'S  GEOMETRY 


47 


righl  angles  to  BD  draw  the  line  CF  indefinitely;  then 
at  the  points  of  intersection  of  the  dotted  lines  will  be 
found  the  points  to  describe  the  required  ellipse. 
A  method  of  describing 
an  ellipse  by  the  intersec- 
tion of  lines  is  shown  at 
Fig.  8,  and  which  may  be 
applied  to  any  kind  of  an 
ellipse  with  longer  or 
shorter  axis.  Let  WX  be 
the  given  major  axis,  and 
YA  the  minor  axis  drawn  at  right  angles  to  and  at  the 
center  of  each  other. 

Through  Y  parallel  to  WX  draw  ZT,  parallel  to  AY, 
draw  WZ  and  XT;  divide  WZ  and  XT  into  any  number 
of  equal  parts,  say  four,  and  draw  lines  from  the  points 

S 


N 

of  division  OOO,  etc.,  to  Y.  Divide  WS  and  XS  each 
into  the  same  number  of  equal  parts  as  WZ  and  XT, 
and  draw  lines  from  A  through  these  las*:  points  o( 
division  intersecting  the  lines  drawn  from  OOO, 
etc.,  and  at  these  intersections  trace  the  semi-ellipse 
WYX.  The  other  half  of  the  ellipse  may  be  described 
in  the  same  manner. 


MODERN  CARPENTRY 


To  describe  an  ellipse  from  given  diameters,  by 
intersection  of  lines,  even  though  the  figure  be  on  a 
rake:  Let  SN  and  QP,  Fig.  9,  be  the  given  diameters, 
drawn  through  the  centers  of  each  other  at  any- 
required  angle.  Draw  QV  and  PT  parallel  to  SN, 
through  S  draw  TV  parallel  to  QP.  Divide  into  any 
number  of  equal  parts  PT,  QV,  PO,  and  OQ;  then 
proceed  as  in  Fig.  8,  and  the  work  is  complete 

An  ellipse  may  be  described  by  the  intersection  of 
arcs  as  at  Fig.  10.  Lay  off  HG  and  JK  as  the  given 
axes;  then  find  the  foci  as  described  in  Fig.  i.  Between 
L  and  L  and  the  cen'«r  M  mark  any  number  of  points 
at  pleasure  as  i,  2,  3,  4.  Upon  L  and  L  with  Hi  for 
radius  describe  arcs  at  O,  O,  O,  O;  upon  L  and  with  Cl 
for  radius  describe  intersecting  arcs  at  O,  O,  O,  and 


O;  then  these  points  of  intersection  will  be  in  the 
curve  of  the  ellipse.  The  other  points  V,  S,  C,  are 
found  in  the  same  manner,  as  follows:  For  the  point 
V  take  H2  for  one  radius,  and  G2  for  the  other;  S  is 
found  by  taking  H3  for  one  radius,  and  G3  for  the 
other;  C  is  found  in  like  manner,  with  ¥4  for  one 
radius,  and  G4  for  the  last  radius,  using  the  foci  for 
centers  as  at  first.  Trace  a  curve  through  the  points 
H,  O,  V,  S,  C,  K,  etc.,  to  complete  the  ellipse. 
It  frequently  happens  that  the  carpenter  has  to  make 


CARPENTER'S  GEOMETRY 


49 


\ 


the  radial  lines  for  the  masons  to  get  their  arches  in 
proper  form,  as  well  as  making  the  centers  for  the 
same,  and,  as  the  obtaining  of  such  lines  for  elliptical 
work  is  very  tedious,  I  illustrate  a  device  that  may 
be  employed  that  will  obviate  a  great  deal  of  labor  in 
producing  such  lines.  The  instrument  and  the 
method  of  using  it  is  exhibited  at  Fig.  ii  and  marked 
Ee.  The  semi-ellipse  HI,  or  xx,  may  be  described 
with  a  string  or  strings,  the  outer  line  being  described 
by  use  of  a  string  fastened  to  the  foci  F  and  D,  with 
the  extreme  point  at  E;  and  the  inner  line,  with  the 
string  being  fastened  at  A  and  B,  with  the  pencil  point 
in  the  tightened  string  at  O.  The  sectional  line  LKJ 
shows  the  center  of  the  arch,  and  the  lines  SSS  are  at 


right  angles  with  this  vertical  line.  The  usual  method 
of  finding  the  normal  by  geometry  is  shown  at  GABC, 
but  the  more  practical  method  of  finding  it  is  by  the 
use  of  the  instrument,  where  Ee  shows  the  normal. 
I  believe  the  device  is  of  French  origin,  and  I  give  a 
translation  of  a  description  and  use  of  the  instrument: 
"It  is  made  of  four  pieces  of  lath  or  metal  put  together 
so  as  to  form  a  perfect  rectangle  and  having  its  joints 
loose,  as  shown  in  the  diagram.  Considering  that  the 
most  perfect  elliptical  curve  is  that  described  by  a 
string  from  the  foci  (foyer)  of  the  ellipse,  draw  the 
profiles  of  the  extrados  and  intrados,  as  shown  in 
Fig.  II,  where  your  joints  are  to  be,  then  take  your 


»'  ■ 


s« 


MODERN  CARPENTRY 


string,  draw  it  to  the  point  marked  as  at  E,  adjust  two 
sides  of  your  instrument  to  correspond  with  the  I'nes 
of  the  string,  then,  from  the  point  marked,   draw  a 

line  passing 
through  the  two 
angles,  E  and  e, 
and  the  line  Ee 
will  be  the  nor- 
mal or  the  radial 
line  sought." 

The  oval  is 
not  an  ellipse, 
nor  ire  any  of 
the  figures  ob- 
tained by  using 
the  compasses, 
as  no  part  of  an 
ff^'  'M         ^'^^vU^  ellipse  is  a  cir- 

cle, though  it 
may  approach  closely  to  it.  The  oval  may  sometimes 
be  useful  to  the  carpenter,  and  it  may  be  well  to  illus- 
trate one  or  two  methods  by  which  these  figures  may 
be  described. 

Let  us  describe  a  diamond  or  lozenge-shaped  figure, 
such  as  shown  at  Fig.  12,  and  then  trace  a  curve  inside 
of  it  as  shown,  touching  the  four  sides  of  the  figure, 
and  a  beautiful  egg-shaped  curve  will  be  formed.  For 
effect  we  may  elongate  the  lozenge  or  shorten  it  at 
will,  placing  the  short  diameter  at  any  point.  This 
form  of  oval  is  much  used  by  turners  and  latiie  men 
generally,  in  the  formation  of  pillars,  balusters,  newel- 
posts  and  turned  ornamental  work  generally. 

An  egg-shaped  oval  may  also  be  inscribed  in  a  figure 
having  two  unequal  but  parallel  sides,  both  of  which 


CARPENTER'S  GEOMETRY 


5» 


are  bisected  by  the  same  line,  perpendicular  to  both 
as  shown  in  Fig.  13.  These  few  examples  are  quite 
sufficient  to  satisfy  the  requirements  of  the  workman, 
as  they  give  the  key  by  which  he  may  construct  any 
oval  he  may  ever  be  called  upon  to  form. 

I  have  dwelt  rather  lengthily  on  the  subject  of  the 
ellipse  because  of  its  being  rather  difficult  for  the 
workman  to  deal  with,  and  it  is  meet  he  should 
acquire  a  fair  knowledge  of  the  methods  of  construct- 
ing it.  It  is  not  my  province 
to  enter  into  all  the  details 
of  the  properties  of  this  very 
intersecting  figure,  as  the 
workman  can  find  many  of 
these  in  any  good  work  on 
mensuration,  if  he  should  re- 
quire more.  I  may  say  here, 
however,  that  geometricians 
so  far  have  failed  to  discover 

any  scientific  method  of  forming  parallel  ellipses,  >o 
that  while  the  inside  or  outside  lines  of  an  ellipse  can 
be  obtained  by  any  of  the  metho'^l>;  I  have  given,  the 
parallel  line  must  be  obtained  either  by  gauging  the 
width  of  the  material  or  space  required,  or  must  be 
obtained  by  "pricking  off"  with  compasses  or  other 
aid.  I  thought  it  best  to  mention  this  as  many  a 
young  mail  has  spent  hours  in  trying  to  solve  the 
unsolvable  problem  when  using  the  pins,  pencil  ?r-J 
string. 

There  are  a  number  of  oth(;r  curves  the  carpenter 
will  sometimes  meet  in  daily  work,  chief  among  these 
being  the  scroll  or  spiral,  so  it  wii!  be  well  for  him  to 
have  some  little  knowledge  of  its  structure.  A  true 
spiral  can  be  drawn  by  unwinding  a  piece  of  string  that 


r/^./j. 


51 


MODERN   CARPENTRY 


V  ■ 


has  been  wrapped  around  a  cone,  and  this  is  probably 
the  method  adopted  by  the  ancients  in  the  formation 
of  the  beautiful  Ionic  spirals  they  producer*      A  spiral 

drawn  by  this 
method  is 
shown  at  Fig. 
14.  This  was 
formed  by  using 
two  lead-pencils 
which  had  been 
sharpened  by 
one  of  those 
patent  sharpen- 
ers and  which 
gave  them  the 
shape  seen  in 
Fig.     15.      A 

*^*       *     ^'**^— — '"^  was    then    tied 

tightly  around  the  pencil,   and  one  end  was  wound 
round  the  conical  end,  so  as  to  lie  in  notches  made  in 
one   of   the   pencils;     the   point   of    a 
second  pencil  was  pierced  through  the 
string  at  a  convenient  point  near  the 
first   pencil,    completing   the    arrange- 
ment shown  in  Fig.  15.     To  draw  the 
spiral  the  pencils  must  be  kept  vertical, 
the  point  of  the  first  being  held  firmly 
ya.    the   hole  of    the    spiral,   and  the 
second   pencil   must    then   be    carried 
around  the  first,  the  distance  between 
the  two  increasing  regularly,  of  course,  as  the  string 
unwinds. 
This    is  a   r«ugh-and-ready  apparatus,  but  a  true 


Fi^J5. 


CARPENTER'S  GEOMETRY 


53 


spiral  can  be  described  by  it  in  a  very  few  minutes. 

By  means  of  a  larger  cone,  spirals  of  any  size  can,  of 

course,  be  drawn,  and  that  portion  of  the  spiral  can  be 

used  which  conforms  to 

the  required  height. 
Another  similar 

method     is     shown    in 

Fig.    i6,    only    in    this 

case  the  string  unwinds 

from  a  spool  on  a  fixed 

center  A,  D,  B.     Make 

loop    E  in   the  end  of 

the    thread,    in    which 

place  a  pencil  as  shown. 

Hold  the  spool    firmly 

and    move    the    pencil 

around     it,    unwinding 

the  thread.     A  curve  will  be  described,  as  shown  in 

the  lines.     It  is  evident  that  the  proportions  of  the 

figure  are  determined  by  the  size  of  the  spool.     Hence 

a  larger  or 
smaller  spool 
is  to  be  used, 
as  circum- 
stances  require. 
A  simple 
method  of 
forming  a  figure 
that  corre- 
sponds   to   the 

spiral  somewhat,  is  shown  in  Fig.  17.     This  is  drawn 

from  two  centers  only,   a  and  e,  and  if  the  distance 

between  these  centers  is  not  too  great,  a  fairly  smooth 

appearance  will  be  given  to  the  figure.     The  method 


54 


MODERN   CARPENTRY 


of  describing  is  simple.  Take  ai  as  radius  and 
describe  a  semi-circle;  then  take  el  and  describe 
semi-circle  12  on  the  lower  side  of  the  line  AB.  Then 
with  a2  as  radius  describe  semi-circle  above  the  line; 
again,  with  e3  as  radius,  describe  semi-circle  below 
the  line  AB;  lastly  with  33  as  radius  describe  semi- 
circle above  the  line. 

In  the  spiral  shown  at  Fig.  18  we  have  one  drawn  in 
a   scientific   manner,    and    which   can   be   formed    to 

dimensions.  T  o 
draw  it,  proceed 
as  follows:  Let 
BA  be  the  given 
breadth,  and  the 
number  of  revolu- 
tions, say  one  and 
three-fourths;  now 
multiply  one  and 
three-  fourths  by 
four,  which  equals 
seven;  to  which 
add  three,  the 
number  of  times  a 
side  of  a  square  is 
contained  in  the 
diameter  of  the 
eye,  making  ten  in 
all.  Now  divide  AB  into  ten  equal  parts  and  set  one 
from  A  to  D,  making  eleven  parts.  Divide  DB  into 
two  equal  parts  at  O,  then  OB  will  be  the  radius  of  the 
first  quarter  OF,  FE;  make  the  side  of  the  square,  as 
shown  at  GF,  equal  to  one  of  the  eleven  parts,  and 
divide  the  number  of  parts  obtained  by  multiplying 
the  revolutions  by  four,  which   is  seven;    make  the 


CARPENTER'S  GEOMETRY 


SS 


diameter  of  the  eye,  12,  equal  to  three  of  the  eleven 
parts.  With  F  as  a  center  and  E  as  a  radius  make  the 
quarter  EO;  then,  with  G  as  a  center,  and  GO  as  a 
radius,  mark  the  quar- 
ter OJ.  Take  the  next 
center  at  H  and  HJL 
in  the  quarter;  so  keep 
on  for  centers,  drop- 
ping one  part  each 
time  as  shown  by  the 
dotted  angles.  Let 
EK  be  any  width  de- 
sired, and  carry  it 
around  on  the  same 
centers. 

Another  method  of 
obtaining  a  spiral  by 
arcs  of  circles  is  shown 
at  Fig.  19,  which  may 
be  confined  to  given  dimensions.  Proceed  as  follows: 
Draw  SM  and  LK  at  right  angles;  at  the  intersection 
of  these  lines  bisect  the  angles  by  the  lines  NO  and 
QP;  and  on  NO  and  QP  from  the  intersection  each 
way  set  off  three  equal  parts  as  shown.  On  i  as  center 
and  iH  as  radius,  describe  the  arc  HK,  on  2  describe 
the  arc  KM,  on  3  describe  the  arc  ML,  on  4  describe 
the  arc  LR.  The  fifth  center  to  describe  the  arc 
RT  is  under  i  on  the  line  QP;  and  so  proceed  to 
complete  the  curve. 

There  are  a  few  other  curves  that  may  occasionally 
prove  useful  to  the  workman,  and  I  submit  an  example 
or  two  of  each  in  order  that,  should  occasion  arise 
where  such  a  curve  or  curves  are  required,  they  may  be 
met  with  a  certain  amount  of  knowledge  of  the  subject. 


s« 


MODERN  CARPENTRY 


I 


^: 


■ 


The  first  is  the  parabola,  a  curve  sometimes  used  in 
bridge  work  or  similar  construction.  Two  examples 
of  the  curve  are  shown  at  Fig.  20,  and  the  methods  of 

describing  them. 
The  upper  one  is 
drawn  as  follows: 
I.  Draw  C8  per- 
pendicular to  AB, 
and  make  it  equal 
to  AD 

Next  join  A8 
anil  B8,  and  divide 
bo;  1  line  into  the 
same  number  of  equal  parts,  say  8;  number  th  m  as  in 
the  figure;  draw  i,  1-2,  .'-3,  3,  etc.,  then  these  lines 
will  be  tangents  to  the  curve;  trace  the  curve  to  touch 
the  center  of  *  ach  of  tho  ■  lines  between  the  points  of 
intersection. 

The  lower  example  is  described  thus:  I.  Divide 
AT)  and  BE,  into  any  number  of  equal  parts;  CD  and 
CE  into  a  simila'  number. 

2.  Draw  I,  1-2,  2,  etc..  parallel  to  AD,  rnd  from  the 
points  of  division  in  AD  and  BE,  draw  lines  to  C. 
Th<  points  of  intersection  of  the  respective  lines  are 
po'  its  in  the  curve. 

The  curves  found,  as  in  these  figu  s,  ar^  quicker  at 
the  crown  than  a  true  circular  segment;  but,  where  me 
rise  of  the  arch  is  not  mon  than  one-tenth  of  th*- 
span,  the  variation  cannot  be  perceived. 

A  raking  example  of  thih  cur\  e  .^  shown  in  Fig.  21 
and  the  method  of  describing  it:     Let  AC  be  the  •  -di- 
nate  or  vertical  line,  and  Dl   the  axis,  and  B  its    cuex; 
produce  the  axis  to  E.  and  make  I'E  equal  to  DB;  j  ;in 
EC,  EA,  and  divide  them  each  into  the  same  r  ^sabtr 


CARPENTER'S  GEOMETRY 


S7 


of  equal  parts,  and  number  the  diviiions  as  shown  on 
the  figures.     Join  th-  corresponding  divisions  by  the 
lines  II,  22,  etc.,  and  their  intersections  will  produte 
the    contour   of 
the  curve. 

The  hyper- 
bola is  some- 
what similar  in 
appear  iHce  t  o 
the  parabola  but 
it  has  properties 
peculiar  to  it- 
self. It  is  a 
dg  rt  not  much 
used  in  carpcn-  4 
fry,  but  it  may 
\     well  to  refer  to  it  br  efly:     Suppose  there  be  two 

rij^ht  equal  cones.  Fig.  22,   hav- 

.^    — ^'  --ji^       ing  tiic  same  axis,  and  cut  by  a 

^  A  J   plane  Mn  ,  Nm,  parallel  to  that 

V- —     [  ^A-jv      axis,    the   sections   MAN,   rana, 
\  \y         which  result,  are  hyperbolas.    In 

\  1  7&  place  <  f  two  cones  opposite  to 

each  other,  geometricians  some- 
times suppose  ioi.  cones,  which 
join  on  thp  lines  EH,  GB,  Fig. 
23.  and  of  which  axis  form  two 
right  lines,  Ff,  FT,  crossing  the 
center  C  in  the  same  plane. 

To  describe   a   cych  id:     The 
cycloid  is  the  curve  describ-'d  by 
a  point  i'-  ■'       Vcumfer^n      of  a 
circle 
and  ' 


I 


. 


58 


MODERN    CARPENTRY 


1.  Let  GH,  Fig.  24,  be  the  edge  of  a  straight  ruler, 
and  C  the  center  of  the  generating  circle. 

2.  Through  C  draw  the  diameter  AB  perpendicular 

to  GH,  and  EF"  parallel  to 
GH;  then  AB  is  the  height 
of  the  curve,  and  EF  is  the 
place  of  the  center  of  the 
generating  circle  at  every 
point  of  its  progress. 

3.  Divide  the  semi-cir- 
cumference from  B  to  A 
into  any  number  of  equal 
parts,  say  8,  and  from  A 
draw  chords  to  the  points 
of  division. 

4.  From  C,  with  a  space 
in  the  dividers  equal  to  one  of  the  divi';'  ins  on  the 
circle,  step  off  on  each  side  the  same  number  of  spaces 
as  the  semi-circumference  is  divided  into,  and  through 
the  points  draw  perpendiculars  to  GH;  number  them 
as  in  the  diagram. 

5.   From    the    points  of  division    in   EF  with   the 


Fig.  2  4. 

radius  of  the  generating  :ircle,  describe  indefinite  arcs 
as  shown  by  the  dotted  lines. 

6.  Take  the  chord  Ai  in  the  dividers,  and  with  the 
foot  at  I  and  i  on  the  line  GH,  cut  the  indefinite  arcs 


CARPENTER'S  GEOMETRY 


59 


described  from  i  and  i  respectively  at  D  and  D',  then 
D  and  D'  are  points  in  the  curve. 

7  With  the  chord  A2,  from  2  and  2  in  GH,  cut  the 
indefinite  arcs  in  J  and  J',  with  the  chord  A3,  from  3 
and  3,  cut  the  arcs  in  K  and  K'  and  apply  the  other 
chords  in  the  same  manner,  cutting  the  arcs  in  LM, 
etc. 

8.  Through  the  points  so  found  trace  the  curve. 


F{g.2S. 


Each  of  the  indefinite  arcs  in  the  diagram  represents 
the  circle  at  that  point  of  its  revolution,  and  the  points 
D.J.K,  etc.,  the  position  of  the  generating  point  B  at 
each  place.  This  curve  is  frequently  used  for  the 
arches  of  bridges,  its  proportions  are  always  constant, 
viz.:  the  span  is  equal  to  the  circumference  of  the 
generating  circle  and  the  rise  equal  to  the  diameter. 
Cycloidal  arches  are  frequently  constructed  which  ar< 


6o 


MODERN  CARPENTRY 


not  true  cycloids,  but  approach  that  curve  in  a  greater 
or  less  degree. 

The  epicycloidal  curve  is  formed  by  the  revolution 
of  a  circle  round  a  circle,  either  within  or  without  its 
circumference,  and  described  by  a  point  B,  Fig.  25,  in 
the  circumference  of  the  revolving  circle,  and  Q  of  the 
stationary  circle. 

The  method  of  finding  the  points  in  the  curve  is  here 
given: 

1.  Draw  the  diameter  8,  8  and  from  Q  the  center, 
draw  QB  at  right  angles  to  8,  8. 

2.  With  the  distance  QP  from  Q,  describe  an  arc  O, 
O  representing  the  position  of  the  center  P  throughout 
its  entire  progress. 

3.  Divide  the  semi-circle  BD  and  the  quadrants  D8 
into  the  same  number  of  equal  parts,  draw  chords 
from  D  to  1,  2,  3,  etc.,  and  from  Q  draw  lines  through 
the  divisions  in  D8  to  intersect  the  curve  OO  in  1, 
2,  3,  etc. 

4.  With  the  radius  of  P  from  I,  2,  3,  etc.,  in  00, 
describe  indefinite  arcs;  apply  the  chords  Dl,  D2,  etc. 
from  I,  2,  3,  etc.,  in  the  circumference  of  Q,  cutting 
the  indefinite  arcs  in  A,C,E,F,  etc.,  which  are  points 
in  the  curve. 

We  are  now  in  a  position  to  undertake  actual  work, 
and  in  the  next  chapter,  I  will  endeavor  to  apply  a  part 
of  what  has  preceded  to  practical  examples,  such  as 
are  required  for  every-day  u?e.  Enough  geometry  has 
been  given  to  enable  the  workman,  when  he  has  mas- 
tered it  all,  to  lay  out  any  geometrical  figure  h«^  may  be 
called  upon  to  execute;  and  with,  perhaps,  the  excep- 
tion of  circular  and  elliptical  stairs  and  hand-railings, 
which  require  a  separate  study,  by  what  has  been  for- 
mulated and  what  will  follow,  he  should  be  able  to  exe- 
cute almost  any  work  in  a  scientific  manner,  that  may 
be  placed  under  his  control.. 


^3 


PART   II 


PRACTICAL   EXAMPLES 
CHAPTER  I 

We  are  now  in  a  position  to  undertake  the  solution 
of  practical  examples,  and  I  will  commence  this 
department  by  offering  a  few  practical  solutions  that 
will  bring  into  use  some  of  the  work  already  known  to 
the  student,  if  he  has  followed  closely  what  has  been 
presented. 

It  is  a  part  of  the  carpenter's  duty  to  lay  out  and 
construct  all  the  wooden  centers  required  by  the  brick- 
layer and  mason  for  turning  arches  over  openings  of 
all  kinds;  therefore,  it  is  essential  he  should  know  as 
much  concerning  arches  as  will  enable  him  to  attack 
the  problems  with  intelligence.  I  have  said  some- 
thing of  arches,  in  Part  I.  but  not  sufficient  to  satisfy 
all  the  needs  of  the  carpenter,  so  I  supplement  with 
the  following  on  the  same  subject:  Arches  used  in 
building  are  named  according  to  their  curves, — cir- 
cular, elliptic,  cycloid,  parabolic,  hyperbolic,  etc. 
Arches  are  also  known  as  three  or  four  centered  arches. 
Pointed  arches  are  called  lancet,  equilateral  and 
depressed.  Voussoirs  is  the  name  given  to  the  stones 
forming  the  arch;  the  central  stone  is  called  the  key- 
stone. The  highest  point  in  an  arch  is  called  the 
crown,  the  lowest  the  springing  line,  and  the  spaces 
between  the  crown  and  springing  line  on  either  side, 
the  haunches  or  flanks.     The  under,  or  concave,  sur- 

6i 


6a 


MODERN  CARPENTRY 


face  of  an  arch  is  called  the  intrados  or  soflfit,  the 
upper  or  convex  surface  is  called  the  extrados.  The 
span  of  an  di  :h  is  the  width  of  the  opening.  The 
supports  of   an  arch  are  called  abutments,  piers,  or 


springing  walls.  This  applies  to  the  centers  of  wood, 
as  well  as  to  brick,  stone  or  cement.  The  following 
six  illustrations  show  the  manner  ri  getting  the  curves, 
as  well  as  obtaining  the  radiating  lines,  which,  as  a 
rule,  the  carpenter  will  be  asked  to  prepare  for  the 
mason.     We  take  them  in  the  following  order: 

Fig.  1.     A  Semi-circular  Arch.— RQ  is  the  span,   and 
the  line  RQ  is  the  springing  line;    S  is  the  center  from 


Fig.  3. 


Fig.4- 


which  the  arch  is  described,  and  to  which  all  joints  of 
the  voussoirs  tend.     T  is  the  keystone  of  the  arch. 

Fig.  2.     A    Segment    Arch.— U   is   the    center    from 
which  the  arch  is  described,  and  from  U  radiate  all 


PRACTICAL   EXAMPLES 


«3 


the  joints  of  the  arch  stones.  The  bed  line  of  the 
arch  OP  or  MN  is  called  by  mason  builders  a  skew- 
back.  OM  is  the  span,  and  VW  is  the  height  or 
versed  sine  of  the  segment  arf-h. 

Figs.  3  and  4.  Moorish  c/  Saracenic  Arches,  one  of 
which  is  pointed.  Fig  3  is  sometimes  called  the 
_^_^_^_^_^_^^.^  horseshoe  arch.  The  springing 
,\\\\in  I  1/777  lines  DC  and  ZX  of  both  arches 
are  below  the  centers  BA  and  Y. 
Fig.  5.  A  Form  of  Lintel  Called  a 
Platband,  built  in  this  form  as  a  substitute  for  a  segment 
arch  over  the  opening  of  doors  or  windows,  generally 
of  brick,  wedge-shaped. 

Fig.  8.    The  Elliptic  Arch.— This  arch    is   most  per- 
fect when  described  with  the  trammel,  and  in  that  case 


1 


rig. 


K 


the  joints  of  the  arch  stones  are  found  as  follows:  Let 
ZZ  be  the  foci,  and  B  a  point  on  the  intrados  where  a 
joint  is  required;  from  ZZ  draw  lines  to  B,  bisect  the 
angle  at  B  by  a  line  drawn  through  the  intersecting 
arcs  D  produced  for  the  joint  to  F.     Joints  at  I  and  3 


MODERN  CARPENTRY 


arc  found  in  the  same  manner.  The  joints  for  the 
opposite  side  of  the  arch  may  be  transferred  as  shown. 
The  semi-axes  of  the  ellipse,  HG,  GK,  are  in  the  same 
ratio  as  GE  to  GA.     The  voussoirs  near  the  springing 


8 — I 


line  of  the  arch  are  thus  increased  in  size  for  greater 
strength.  I  gave  a  very  good  description  of  this 
latter  arch  in  Part  I,  which  see. 

Another  series  of  arches,  known  as  Gothic  arches, 
are  shown  as  follows,  with  all  the  centers  of  the  curve 
given,  so  that  their  formation  is  rendered  quite  simple. 
The  arch  shown  at  Fig.  ;  is  equilateral  and  its  out- 
lines have  been  shown  before.  I  repeat,  however,  let 
AB  be  the  g-ven  span;  on  A  and  B  as  centers  with 
AB  as  radius,  describe  the  arcs  AC  and  BC. 

The  lancet  arch.  Fig.  8,  is  drawn  as  follows:  DE  is 
the  given  span;  bisect  DE  in  J,  make  DF  and  EG 
equal  DJ;   on  Fas  center  with  FE  as  radius  describe 


Tig.  9      '  I        Fig.  10 

the  arc  EH,  and  on  G  as  center  describe  the  arc  DH. 
A  lancet  arch,  not  so  acute  as  the  previous  one,  is 


PRACTICAL  EXAMPLES 


<5 


shown  at  Fig.  9.  Let  KL  be  the  given  span;  bisect 
KL  in  M,  make  MP  at  right  angles  to  KL  and  of  the 
required  height;  connect  LP,  bisect  LP  by  a  line 
through  the  arcs  R,  Q  produced  to  N;  make  MO  equal 
MN;  with  N  and  O  as  centers,  with  NL  for  radius 
describe  the  arcs  KP  and  LP.  Fig.  10  shows  a  low 
or  drop  arch,  and  is  obtained  as  follows:  Let  ST  be 
the  given  span,  bisect  ST  in  W;  let  WX  be  the 
required  height  at  right  angles  to  TS;   connect  TX, 


bisect  TX  by  a  line  through  the  arcs  YZ  produced  to 
V,  make  TU  equal  SV;  on  V  and  U  as  centers  with 
VT  as  radius  describe  the  arcs  TX  and  SX.  Another 
Gothic  irch  with  a  still  less  height  is  shown  at  Fig. 
II.  Suppose  AB  to  be  the  given  span;  then  divide 
AB  into  four  equal  parts;  make  AF  and  BG  equal 
AB,  connect  FE  and  produce  to  D;  with  CA  as  radius, 
on  C  and  E,  describe  the  arcs  AD  and  BK;  on  F  and 
G  as  centers,  describe  the  arcs  JK  and  DK. 

Another  four-centered  arch  of  less  height  is  shown 
at  Fig.  12.  Let  SI  be  the  given  span,  divide  into  six 
equal  parts;  on  R  and  Q  as  centers  with  RQ  as  radius 
describe  the  arcs  QV  and  RV,  connect  QV  and  RV  and 
produce  to  L  and  M;  on  R  and  Q  as  centers  with  QT  as 


66 


MODERN   CARPENTRY 


radius  describe  the  arcs  TP  and  SO;   on  L  and  M  as 
centers  describe  the  arcs  PN  and  ON. 

To  describe  an  equilateral  Ogee  arch,  like  Fig.  13, 
proceed  as  follows:     Make  YZ  the  given  span;  make 


YX  equal  YZ,  bisect  YZ  in  A;  on  A  as  center  with 
AY  as  radius  describe  the  arcs  YB  and  ZC;  on  B  and 
X  as  centers  describe  the  arcs  BD  and  XD,  and  on  C 
and  X  as  centers  describe  the  arcs  CE  and  XE,  on  E 
and  D  as  centers  describe  the  arcs  BX  and  CX. 

Fig.  14  shows  the  method  of  obtaining  the  lines  for 
an  Ogee  arch,  having  a  height  equal  to  half  the  span 
Suppose  FH  to  be  the  span,  divide  into  four  equal 
parts,  and  at  each  of  the  points  of  division  draw  lines 
LN,  KG  and  JO  at  right  angles  to  FH;  with  LF  for 
radius  on  L  and  J  describe  the  quarter  circles  FM  and 
HP;  and  with  the  same  radius  on  O  and  N  describe 
the  quarter  circles  PG  and  MG. 

These  examples-all  or  any  of  them— can  be  made  use 
of  in  a  great  number  of  instances.  Half  of  the  Ogee 
curve  is  often  e^nployed  for  veranda  rafters,  as  for  the 
roofs  of  bay-windows,  for  tower  roois  and  for  bell 
bases,  for  oriel  and  bay-windows,  and  many  other 
pieces  of  work  the  carpenter  will  be  confronted  with 
from  tunc  to  time.  They  aiso  have  value  as  aids  in 
forming  mouldings  and  other  ornamental  work,  as  for 


i.'iasj''!i»ffiiir*?awBffBi».v,at-.--i*jlte!.-  "'' 


J 


•TTTi^Kw^S^rfre^^TT^ 


PRACTICAL  EXAMPLES 


67 


example  Fig.  15,  which  shows  a  moulding  for  a  base 
or  other  like  purpose.  It  is  described  as  follows: 
Draw  AB;  divide  it  into  five 
equal  parts;  make  CD  equal  to 
four  of  these.  Through  D  draw 
DF  parallel  with  AB.  From  D, 
with  DC  as  radius,  draw  the  arc 
CE.  Make  EF  equal  to  DE;  di- 
vide EF  into  five  parts;  make  the 
line  above  F  equal  to  one  of  these; 
draw  FG  equal  to  six  of  these. 
From  G,  with  radius  DE,  describe 
the  arc;  bisect  GF,  and  lay  the 
distance  to  H.  It  is  the  center  of 
the  curve,  meeting  the  semi-circle 
described  from  M.  Join  NO,  OS, 
and  the  moulding  is  complete. 

The  two  illustrations  shown  at 
Figs.  16  and  17  will  give  the  stu- 
dent an  idea  of  the  manner  in 
which  he  can  apply  the  knowledge  he  has  now  obtained, 
and  -'t  may  not  be  out  of  place  to  say  that  with  a  little 
ingenuity  he  can  form  almost  any  sort  of  an  ornament 
he  wishes  by  using  this  knowledge.  The  two  illustra- 
tions require  no  explanation  as  their  formation  is  self- 
evident.  Newel  posts,  balusters,  pedestals  and  other 
turned  or  wrought  ornaments,  maybe  designed  easily 
if  a  little  thought  be  brought  to  bear  on  the  subject. 

The  steel  square  is  a  great  aid  in  working  out  prob- 
lems in  carpentry,  and  I  will  endeavor  to  show,  as 
briefly  as  possible,  how  the  square  can  be  applied  to 
some  difficult  problems,  and  insure  correct  solutions. 

It  is  unnecessary  to  give  a  full  and  complete  descrip- 
tion of  the  steel  square.    Every  carpenter  and  joiner  is 


•  f 


68 


MODERN  CARPENTRY 


supposed  to  be  the  possessor  of  one  of  these  useful 
tools,  and  to  have  some  knowledge  of  using  it.  It  is 
not  everyone,  however,  who  thoroughly  understands 
its  powers  or  knows  how  to  employ  it  in  solving  all 


:  I  li- 


the difficulties  of  framing,  or  to  take  advantage  of  its 
capabilities  in  laying  out  work.  Whi'e  it  is  not  my 
intention  to  go  deeply  into  this  subject  in  this  vol- 
ume, as  that  would  lengthen  it  out  to  unreasonable 
limits,  so  it  must  be  left  for  a  separate  work,  yet  there 
are  some  simple  things  connected  with  the  steel  square, 
that  I  think  every  carpenter  and  joiner  should  know, 
no  matter  whether  he  intends  to  go  deeper  into  the 
study  of  the  steel  square  or  not.  One  of  these  things 
is  the  learning  to  read  the  tool.     Strange  as  it  may 


PRACTICAL  EXAMPLES 


<9 


appear,  not  over  one  in  fifty  of  those  who  ivse  the 
square  are  able  to  read  it,  or  in  other  words,  able  to 
explain  the  meaning  and  uses  of  the  figuies  stamped 
on  its  two  sides.  The  following  will  assist  the  young 
fellows  who  want  to  master  the  subject. 

The  square  consists  of  two  arms,  at  right  angles  to 
each  other,  one  of  which  is  called  the  blade  and  which 
is  two  feet  long,  and  generally  two  inches  wide.  The 
other  arm  is  called  the  tongue,  and  may  be  any 
length  from  twelve  to  eighteen  inches,  and  i^  to 
2  inches  in  width.  The  best  square  has  always  a 
blade  2  inches  wide.  Squares  made  by  firms  of  repute 
are  generally  perfect  and  require  no  adjusting  or 
"squaring." 

The  lines  and  figures  formed  on  squares  of  different 
make  sometimes  vary,  both  as  to  their  position  on  the 
square  and  their  mode  of  application,  but  a  thorough 
understanding  of  the  application  of  the  scales  and 
lines  shown  on  any  first-class  tool,  will  enable  the  stu- 
dent to  comprehend  the  use  of  the  lines  and  figures 
exhibited  on  any  good  square. 

It  is  supposed  the  reader  understands  the  ordinary 
divisions  and  subdivisions  of  the  foot  and  inch  into 
twelfths,  inches,  halves,  quarters,  eighths  and  six- 
teenths, and  that  he  also  understands  how  to  use  that 
part  of  the  square  that  is  subdivided  into  twelfths  of 
an  inch.  This  being  conceded,  we  now  proceed  to 
describe  the  various  rules  as  shown  on  all  good  squares. 
Sometimes  the  inch  is  subdivided  into  thirty-seconds, 
in  which  the  subdivision  is  very  fine,  but  this  scale 
will  be  found  very  convenient  in  the  measure- 
ment ot  drawings  which  are  made  to  a  scale  of 
half,  quarter,  one-eighth  or  one-sixteenth  of  an  inch 
to  a  foot. 


7« 


MODERN  CARPENTRY 


In  the  illustration  Fig. 
iS,  will  )C  noticed  a  series 
of  lin<-s  extending  irom 
the  junction  of  the  blade 
and  tongue  to  the  fnur- 
inch  limit.  From  the 
figures  2  to  3  tht'^'-  lines 
are  crossed  by  diatjonal 
lines.  This  figure,  i  ach- 
ing from  2  to  4.  is  c.nlled 
a  diagonal  cale,  and  i=; 
intended  for  takmp  off  hundredths  of  an   inch      The 

vn 


s.i.i 


Fig.  19 


iJilllltilllillll 


;;»ii      ^am  ( 


I 


lengths  of  the  lines  between  the 
diagonal  and  the  perpr  iicular 
aremarkedon  the  latter.  Primary 
divisions  are  tenths,  and  the  junc- 
tion of  the  diagonal  lines  wf^h  the 
longitudinal  parallel  lines  enables 
the  operator  to  obtain  divisions  of 
one-hundredth  part  of  an  inch;  as 
for  example,  if  we  wish  to  obtain 
twenty-four  hundredths  we  operate 
on  the  seventh  line,  taking  five 
^r'Tiaries  and  the  fraction  of  the 

jt 

sixth    where    the  diagonal   inter- 
sects me  parallel  line,  as  shown 


mm 


PRACTICAL  EXAMPLES 


7« 


by  the  "dots"  on  the  compasses,  and  this  gives  us  tht 
distance  required. 

The  ISO  ot  the  scale  is  obvious,  nnd  needs  no  further 
explanation,  as  the  dots  or  points  an.  shown. 

Thu  lines  of  figures  running  across  the  b'ade  of  the 
square,  as  shown  in  Fig.  19,  forms  what  is  .  very  con- 
venient rule  for  det'^-  fining  the  amov.u.  of  n^itt .  iai  m 
length  or  wid'h  .)i  it  tfi      To  use  ir  proc<        as  fol- 
lows:    If  we  examine  we  will  find  under  the  figure  12, 
on    he  outer  cdsf..-  of  the  blade   ,vhere  the  lerp'h  of  .he 
boards,  plank  (ir  scantling  to  be  measup'f    .s  given, 
and  the  an-.ver  in  feet  and  inches  is  founc     under  the 
inches  ir    width  that  the  board,  etc.,  n  casures.     For 
examp!  ,  take  a  b<uird  nine  feet  long  and  five  inches 
wide,  then  under  the  figure   12,   on  the  second  line, 
will  be  found  the  figure  9,  Wi.ich  is  the  length  of  the 
bop.-d;   then  run  along  this  line  to  the  figure  directly 
under  the  five  inches  (the  width  of  the  board)  and  we 
find  three  feet  nine  inches,  which  is  the  correct  answer 
in  '  board  measure."     If  the  stuff  is  three  inches  thick 
it  i>  *.. '))  •  :    etc.,  etc.     If  the  stuff  is  longer  than  any 
fip.ii       shown   on  the  square  it   can   be  measured  as 
above   and   doubling   the   result.     This  rule  is  calcu- 
lated, as  its  name  indicates,  for  board  measure,  or  for 
surfaces  i  inch  in  thickness.     It  may  be  advantageously 
used,  however,  upon  timber  by  multiplying  the  result 
rf  the  face  measure  of  one  side  of  a  piece  by  its  depth 
in   inches.     To  illustrate,   suppose   it   be  required  to 
measure  a  piece  25  feet  long,    10x14  inches  in  size. 
For  the  length  we  will  take   12  and  13  feet.     For  the 
width  we  will  take   10  inches,  and  multiply  the  result 
by  14.     By  the  rule  a  board  12  feet  long  and  10  inches 
wide  contains   10  feet,  and  one   13  feet  long  and  10 
inches  wide,  lo  feet  10  inches.     Therefore,  a  board  25 
teet  long  and  10  inches  wide  must  contain  20  feet  and 


7a 


MODERN  CARPENTRY 


f 


10  inches.  In  the  timber  above  described,  however, 
we  have  what  is  equivalent  to  14  such  boards,  and 
therefore  we  multiply  this  result  by  14,  which  gives 
291  feet  and  8  inches  the-board  measure. 

Along  the  tongue  of  the  square  following  the  diag- 
onal scale  is  the  brae*  rule,  which  is  a  very  simple  and 
very  convenient  method  of  determining  the  length  of 
any  brace  of  regular  run.  The  le.igth  of  any  brace 
simply  represents  the  hypothenuse.  of  a  right-angled 
triangle.  To  find  the  hypothenuse  extract  the  square 
root  of  the  sum  of  the  squares  of  the  perpendicular 
and  horizontal  runs.  For  instance,  if  6  feet  is  the 
horizontal  run  and  8  feet  the  perpendicular,  6  squared 
equals  36,  8  squared  equals  64;  36  plus  64  equals  100, 
the  square  root  of  which  is  10.  These  are  the  rules 
generally  used  for  squaring  the  frame  of  a  building. 

If  the  run  is  42  inches,  42  squared  is  1764,  double 
that  amount,  both  sides  being  equal,  gives  3528,  the 
square  root  of  which  is,  in  feet  and  inches,  4  feet  11.40 
inches. 

In  cutting  braces  always  allow  in  length  from  a  six- 
teenth to  an  eighth  of  an  inch  more  than  the  exact 
measurement  calls  for. 

DirecMy  under  the  half-inch  marks  on  the  outer  edge 
of  the  back  of  the  tongue,  Fig.  19,  will  be  noticed  two 
figures,  one  above  the  other.  These  represent  the  run 
of  the  brace,  or  the  length  of  two  sides  of  a  right- 
angled  triangle;  the  figures  immediately  to  the  right 
represent  the  length  of  the  brace  or  the  hypothenuse. 
For  instance,  the  figures  I],  and  80.61  show  that  the  run 
on  the  post  and  beam  is  57  inches,  and  the  length  of  the 
brace  is  8o.6l  inches. 

Upon  some  squares  will  be  found  brace  measure- 
ments given,  where  the  run  is  not  equal,  as  JJ.30.  It 
will  be  noticed  that  the  last  set  of  figures  are  each  just 


PRACTICAL  EXAMPLES 


73 


three  times  those  mentioned  in  the  set  that  are  usually 

used  in  squaring  a  building.      So  if  the  student  or 

mechanic  will  fix 

in    his    mind    the 

measurements  of  a 

few  runs,  wich  the 

length   of   braces, 

he   can   readily 

work    almost   any 

length  required. 

Take  a  run,  for 
instance,  of  9 
inches  on  the 
beam  and  12 
inches  on  the  post. 
The  1  e  n  gt  h  of 
brace  is  15  inches.  In  a  run,  therefore,  of  12,  16,  20,  or 
any  number  of  times  above  the  figures,  the  length  of 
the  brace  will  bear  the  same  proportion  to  the  run  as 
the  multiple  used.  Thu-^  if  you  multiply  all  the  fig- 
ures by  3  you  will  have  36  and  48  inches  for  the  run, 
and  60  inches  for  the  brace,  or  to  remember  still  more 
easily,  3,  4  and  5  feet. 

There  is  still  another  and  an  easier  method  of  obtain- 
ing the  lengths  of  braces  by  aid  of  the  square,  also  the 
bevels  as  may  be  seen  in  Fig.  20,  where  the  lun  is  3 
feet,  or  36  inches,  as  marked.  The  length  and  bevels 
of  the  brace  are  found  by  applying  the  square  three 
times  in  the  position  as  shown;  placing  12  and  12  on 
the  edge  of  the  timber  each  time.  By  this  method 
both  length  and  bevel  are  obtained  with  the  least 
amount  of  labor.  Braces  having  irregular  runs  may 
be  ooerated  in  the  same  manner.  For  instance,  sup- 
pose we  wish  to  set  in  a  brace  where  the  run  is  4 
feet  and   3   feet;    we   simply   take  g   inches  on  the 


74 


MODERN   CARPENTRY 


tong^ue  and   12   inches  on   the  blade  and  apply  the 

square  four  times,  as  shown  in 
Fig.  21,  where  the  brace  is 
given  in  position.  Here  we 
get  both  the  proper  length  and 
the  exact  bevels.  It  is  evident 
from  this  tha*  braces,  regular 
or  irregular,  and  of  any  length, 
may  be  obtained  with  bevels  for 
same  by  this  method,  only  care 

Pmust  be  taken  in  adopting  the 
figures  for  the  purpose. 
If  we  want  a  brace  with  a  two- 
foot  run  and  a  four-foot  run,  it  must  be  evident  that 
as  two  is  the  half  of  four,  so  on  the  square  take  12 
inches  on  the  tongue,  and  6  inches  on  the  blade,  apply 
four  times  and  we  have  the  length  and  the  bevels  of  a 
brace  for  this  run. 

For  a  three-by-four  foot  run  take  12  inches  on  the 
tongue  and  g  inches  on  the  blade,  and  apply  four 
times,  because  as  3  feet  is  ^  of  four  feet,  so  9  inches 
is  ^  of  12  inches. 

While  on  the  subject  of  braces  I  submit  the  follow- 
ing table  for  determining  the  length  of  braces  for  any 
run  from  six  inches  to  fourteen  feet.  This  table  has 
been  carefully  prepared  and  may  be  depended  upon  as 
giving  correct  measurements.  Where  the  runs  are 
regular  or  equal  the  bevel  will  always  be  a  miter  or 
angle  of  45°,  providing  always  the  angle  which  the 
brace  is  to  occupy  is  a  right  angle — a  "square."  If 
the  run  is  not  equal,  or  the  angle  not  a  right  angle, 
then  the  bevels  or  "cuts"  will  not  be  miters,  and  will 
have  to  be  obtained  either  by  taking  figures  on  the 
square  or  by  a  scaled  di.igram. 


PRACTICAL   EXAMPLES 


75 


TABLE 


LENCTH 

OF 

Length  or 

LBNOTR  or 

Lkncth  or 

KUN 

BllACB 

Run 

BUACB 

n.   In. 

ft.  In. 

ft. 

In. 

ft.  In. 

ft.  In. 

ft.      In. 

6  X 

6 

= 

8.48 

4  3  X 

4  3 

= 

6     0.12 

6  X 

9 

= 

10.81 

4  3  X 

46 

= 

6    2.27 

9  X 

9 

a 

I 

0.72 

4  3  X 

4  9 

= 

6    4.49 

I     0    X 

I    0 

= 

I 

4-97 

4  3  X 

5  0 

= 

6    6.74 

1    0    X 

I  3 

= 

I 

7.20 

4  6  X 

46 

= 

6    4.36 

I  3  X 

I  3 

= 

1 

9-23 

4  6  X 

4  9 

= 

6    6.51 

1   3  X 

I  6 

= 

I 

11.43 

4  6  X 

5  0 

= 

6    8.72 

I  6  X 

I  6 

=s 

2 

1.45 

4  9  X 

4  9 

= 

6    8.61 

I  6  X 

I  9 

= 

2 

3.65 

4  9  X 

5  0 

= 

6  10.75 

I  9  X 

I  -) 

= 

2 

5.69 

5  0  X 

5  0 

S3 

7    0.85 

I  9  X 

2  0 

= 

2 

7.89 

5  3  X 

5  1 

S3 

7    509 

2  0   X 

2  0 

= 

2 

9.94 

5  6  X 

56 

a 

7    9-33 

2   0   X 

2  3 

=: 

3 

0.12 

5  9  X 

5  9 

8    1.58 

2  0  X 

2  6 

Z3 

3 

2.41 

6  0  X 

6  0 

8    5.82 

2  3  X 

2   6 

= 

3 

4.36 

6  3  X 

63 

8  10.06 

2  6  X 

2  6 

= 

3 

6.42 

6  6  X 

6  6 

9    2.30 

2   6    X 

2   9 

= 

3 

8.59 

6  9  X 

69 

9    6.55 

2  9  X 

2  9 

= 

3 

10.66 

7  0  X 

7  0 

9  10.79 

2  9  X 

3  0 

=3 

4 

0.83 

7  3  X 

7  3 

10    3.03 

3  0  X 

3  0 

= 

4 

2.91 

7  6  X 

76 

10    7.28 

3  0  X 

3  3 

B 

4 

5.02 

7  9  X 

7  9 

s 

10  11.52 

3  0  X 

36 

=: 

4 

7-31 

8  0  X 

8  0 

= 

II    376 

3  0  X 

3  9 

= 

4 

9.62 

8  3  X 

8  3 

= 

II    8.00 

3  3  X 

3  3 

B3 

4 

7.15 

8  6  X 

8  6 

= 

12    0.24 

3  3  X 

36 

= 

4 

9.31 

8  9  X 

89 

= 

12    4.49 

3  3  X 

3  9 

= 

4 

11.54 

9  0  X 

9  0 

= 

12    8.73 

3  3  X 

4  0 

= 

5 

1.84 

9  6  X 

96 

= 

13      5-22 

3  6  X 

36 

= 

4 

11-39 

10  0  X 

10  0 

- 

14      1.70 

3  6  X 

3  9 

= 

5 

1-55 

10  6  X 

10  6 

s: 

14   10.19 

3  6  X 

4  0 

= 

5 

3-78 

11  0  X 

II  0 

= 

15     6.67 

3  9  X 

3  9 

= 

5 

3.63 

II  6  X 

II  6 

ES 

16     3.16 

3  9  X 

4  0 

= 

5 

5  79 

12   0    X 

12  0 

=5 

16   11.64 

4  0  X 

4  0 

= 

5 

7.88 

12    6    X 

12  6 

C3 

17     8.13 

4  0  X 

4  3 

= 

5 

10.03 

13  0  X 

13  0 

= 

18     4.61 

4  0  X 

46 

as 

6 

0.25 

13  6  X 

13  6 

= 

19     I. 10 

4  0  X 

4  9 

» 

6 

2.51 

14  0   X 

14  0 

= 

19  9.58 

4  0  X 

5  0 

= 

6 

4.83 

76 


MODERN  CARPENTRY 


IT 


n 


rrr 


c? 


JJX 


*r 


1 1 1  m.M  1 1  rrrn 


Fig.  22; 


There  is  on  the 
tongue  of  the  square 
a  scale  called  the 
"octagonal  scale." 
This  is  generally  on 
the  opposite  side  to 
Fig.  22  exhibits  a  por- 
Itis 


the  scales  shown  on  Fig.  19. 
tion  of  the  tongue  on  which  this  scale  is  shown 
the  central  division  on  which  the  number  10 
is  seen  along  with  a  number  of  divisions. 
It  is  used  in  this  way:  If  you  have  a  stick 
10  inches  square  which  you  wish  to  dress  up 
octagonal,  make  a  center  mark  on  each 
face,  then  with  the  compasses,  take  10  of  the 
spaces  marked  by  the  short  cross-lines  in  the 
middle  of  the  scale,  and  layoff  this  distance 
each  side  of  the  center  lines,  do  the  same  at 
the  other  end  of  the  stick,  and  strike  a  chalk 
line  through  these  marks.  Dress  off  the  cor- 
ners to  the  lines,  and  the  stick  will  be  octag- 
onal. If  the  stick  is  not  straight  it  must  be 
gauged,  and  not  marked  with  the  chalk  line. 
Always  take  a  number  of  spaces  equal  to  the 
square  width  of  the  octagon  in  inches.  This 
scale  can  be  used  for  large  octagons  by 
doubling  or  trebling  the  measurements. 

On  some  squares,  there  are  other  scales, 
but  I  do  not  advise  the  use  of  squares  that 
are  surcharged  with  too  many  scales  and  fig- 
ures,as  they  lead  toconfusion  and  lossof  time. 

It  will  now  be  in  order  to  offer  a  few 
things  that  can  be  done  with  the  steel 
square,  in  a  shorter  time  than  by  applying 
any  other  methods.     If  we  wish  to  get  the 


^ 


<<^ 


\. 


<-. 


\ 


h 

Fig.  23. 


PRACTICAL   EXAMPLES 


77 


length  and  bevels  for  any  common  rafter  it  can  be  done 
on  short  notice  by  using  the  square  as  shown  in 
Fig.  23.  The  pitch  of  the  roof  will,  of  course,  gov- 
ern the  figures  to  be  employed  en  the  blade  and  tongue. 
For  a  quarter  pitch,  the  figures  must  be  6  and  12.  For 
half  pitch,  12  and  12  must  be  used.  For  a  steeper 
pitch,  12  and  a  larger  figure  must  be  used  according 
to  the  pitch  required.  For  the  lower  pitches,  8  and 
12  gives  a  one-third  pitch  and  9  and  12  a  still  steeper 
pitch;  and  from  this  the  workman  can  obtain  any  pitch 
he  requires.  If  the  span  is  24  feet,  the  square  must  be 
applied  12  times,  as  12  is  half  of  24.  And  so  with 
any  other  span:  The  square  must  be  applied  half  as 
many  times  as  there  are  feet  in  the  width.  This  is 
self-evident.  The  bevels  and  lengths  of  hip  and  val- 
ley rafters  may  be  obtained  in  a  similar  manner,  by 
first  taking  the  length  of  the  diagonal  line  between  12 
and  12,  on  the  square,  which  is  17  inches  in  round 
numbers.  Use  this  figure  on  the  blade,  and  the  "rise" 
whatever  that  may  be,  on  the  tongue.  Suppose  we 
have  a  roof  of  one -third  pitch,  which  has  a  span 
of  24  feet;  then  8,  which  is  one-third  of  24,  will  be 
the  height  of  the  roof  at  the  point  or  ridge,  from  the 
base  of  the  roof  on  a  line  with  the  plates.  For 
example,  always  use  8,  which  is  one-third  of  24,  on 
tongue  fcr  altitude;  12,  half  the  width  of  24,  on  blade 
for  base.  This  cuts  common  rafter.  Next  is  the  hip 
rafter.  It  must  be  understood  that  the  diagonal  of  12 
and  12  is  17  in  framing,  as  before  stated,  and  the  hip 
is  the  diagonal  of  a  square  added  to  the  rise  of  roof; 
therefore  we  take  8  on  tongue  and  17  on  blade;  run 
the  same  number  of  times  as  common  rafter.  To  cut 
jack  rafters,  divide  the  number  of  openings  for  com- 
mon rafter.     Suppose  wc  have  5  jacks,  with  six  open- 


J^ 


J  « 


* 


7«  MODERN  CARPENTRY 

ings,  our  common  rafter  12  feet  long,  each  jack  would 
be  2  feet  shorter,  first  10  feet,  second  8  feet,  third  6 
feet,  and  so  on.  The  top  down  cut  the  same  as  cut  of 
common  rafter;  foot  also  the  same.  To  cut  miter  to 
fit  hip:  Take  half  the  width  of  building  on  tongue  and 
length  of  common  rafter  on  blade;  blade  gives  cut. 
Now  find  the  diagonal  o  8  and  12,  which  is  M^^V.  take 
12  on  tongue,  14^^  on  blade;  blade  gives  cut.  The 
hip  rafter  must  be  beveled  to  suit;  height  of  hip  on 
tongue,  length  of  hip  on  blade;  tongue  gives  bevel. 
Then  we  take  8  on  tongue,  8ji  on  blade;  tongue  gives 
the  bevel.  Those  figures  will  span  all  cuts  in  putting 
on  cornice  or  sheathing.  To  cut  bed  moulds  for  gable 
to  fit  under  cornice,  take  half  width  of  building  on 

^^ tongue,    length  of 

common     rafter    on 

blade;  blade  gives 
cut;  machine  mould- 
ings will  not  mem- 
ber, but  this  gives  a 
solid  joint;  and  to 
member  properly  it 
is  necessary  to  make  moulding  by  hand,  the  diagonal 
plumb  cut  differences.  To  cut  planceer  to  run  up 
valley,  take  height  of  rafter  on  tongue,  length  of  rafter 
or.  blade;  tongue  gives  cut.  The  plumb  cut  takes  the 
height  of  hip  rafter  on  tongue,  length  of  hip  rafter  on 
blade;  tongue  gives  cut.  These  figures  give  the  cuts 
for  one-third  pitch  only,  regardless  of  width  of  build- 
ing. The  construction  of  roofs  generally  will  be  taken 
up  in  another  chapter. 

A  ready  way  of  finding  the  length  and  cuts  for  cross- 
bridging  is  shown  at  Fig.  24.  If  the  joists  are  8  inches 
wide  and  16  inches  centers,   there  will   be   14   inches 


^iVL 


Bb^ 


PRACTICAL  EXAMPLES 


79 


til 


Fig.  25, 


between.  Place  the  square  on  8  and  14,  and  cut  on  8, 
and  you  have  it.  The  only  point  to  observe  is  that  the 
8  is  on  the  lower  side  of  the  piece  of  bridging,  while  the 
14  is  on  the  upper,  and  not  both  on  same  side  of  tim- 
ber, as  in  nearly  all  work.  Bridging  for  any  depth  of 
joists,  to  any  rea- 
sonable distance  of 
joists  apart,  may  be 
obtained  by  this 
method.  A  quick 
way  of  finding  the 
joists  for  laying  out 
timber  to  be  worked  from  the  square  to  an  octagon  sec- 
tion is  shown  at  Fig.  25.  Lay  your  square  diagonally 
across  your  timber  and  mark  at  7  and  17,  which  gives 
corner  of  octagon.  The  figures  7  and  17,  on  either 
a  square  or  two-foot  pocket  rule,  when  laid  on  a  board 
or  piece  of  timber  as  shown,  always  define  the  points 
where  the  octagonal  angle  or  arris  should  be. 

Fig.  26  shows  A 
rapid  method  of 
dividing  anything 
into  several  equal 
parts.  If  the  board 
is  io>4  inches  wide, 
lay  the  square  from 
heel  to  12,  and  mark  at  3,  6  and  g,  and  you  have  it 
divided  into  four  equal  parts.  Any  width  of  board  or 
any  number  of  parts  may  be  worked  with  accuracy 
under  the  same  method. 

A  method  for  obtaining  the  "cuts"  for  octagon  and 
hexagon  joints  is  shown  at  Fig.  27.  Lay  off  a  quarter 
circle  XA,  with  C  as  a  center;  then  along  the  hori- 
zontal line  AB  the  square  is  laid  with  12"  on  the  blade 


Fig.  26 


jfiiStt' 


So 


MODERN   CARPENTRY 


at  the  center  C,  from  which  the  quadrant  was  struck. 
If  we  divide  this  quadrant  into  halves,  we  get  the  point 
E,  and  a  line  drawn  from  12"  on  the  blade  of  the 
square  and  through  the  point  E,  we  cut  the  tongue  of 
the  square  at  12"  and  through  to  O,  and  the  line  thus 
drawn  makes  an  angle  of  45°,  a  true  miter.  If  we 
divide  the  quadrant  between  E  and  X,  and  then  draw 
a  line  from  C,  and  12"  on  the  blade  of  the  square,  cut- 
ting the  dividing  point  D,  we  get  the  octagon  cut, 
which  is  the  line  DC.     Again,  if  we  divide  the  space 


W^ 


between  E  and  X  into  three  equal  parts,  making  GC 
one  of  these  parts,  and  draw  a  line  from  C  to  G  cutting 
the  tongue  of  the  square  at  7",  we  get  a  cut  that  will 
give  us  a  miter  for  a  hexagon;  therefore,  we  see  from 
this  that  if  we  set  a  steel  square  on  any  straight  edge 
or  straight  line,  12"  and  12"  on  blade  and  tongue  on 
the  line  or  edge,  we  get  a  true  miter  by  marking  along 
the  edge  of  the  blade.  For  an  octagon  miter,  we  set 
the  blade  on  the  line  at  12",  and  the  tongue  at  5'',  and 
we  get  the  angle  on  the  line  of  the  blade — nearly;  and, 
for  a  hexagon  cut,  we  place  the  blade  at  12"  on  the 


L-»#*- 


PRACTICAL   EXAMPLES 


8i 


line,  and  the  tongue  at  j",  and  the  line  of  the  blade 
gives  the  angle  of  cut — nearly.  The  actual  figure  for 
octagon  is  45  J,  but  5"  is  close  enough;  and  for  a  hexa- 
gon cui,  the  exact  figures  are  12"  and  b\\,  but  12"  and 
7"  is  as  near  as  most  workmen  will  require,  unless  the 
cut  is  a  very  long  one. 

Ti  e  diagram  shown  at  Fig.  28  illustrates  a  method 
of  defining  the  pitches  of  roofs,  and  also  gives  the  fig- 
ures on  the  square  for  laying  out  the  rafters  for  such 
pitches.  By  a  very  common  usage  among  carpenters 
and  builders,  the  pitct.  of  a  roof  is  described 
by  indicating  what  fraction  the  rise  is  of  the 
span  If,  for  example,  the  span  is  24  feet 
(and  here  it  chould  be  remarked  that  the  dia- 
gram shows  only  one-half  the  span),  then  6 
feet  rise  would  be  called 
quarter  pitch,  because  6  is 
one-quarter  of  .?4.  The  rule, 
somewhat  arbitrarily  ex- 
pressed,   that    is    applicable 


1  1  1  n  I  I  .  I 
*  a  i*  iV  1 


in  such  cases  in  roof  framing  where  the  roof  is  one. 
quarter  pitch,  is  as  follows:  Use  12  of  the  blade,  and 
6  of  the  tongue.  For  other  pitches  use  the  figures 
.'ippropriate  thereto  in  the  sane  general  manner. 

The  d'  i:;ram  indicates  the  figures  for  sixth  pitch, 
quarter  pitch,  third  pitch  and  half  nitch.  Tne  first 
three  of  these  are  in  viry  comm-in  uc,  although  the 
latter  is  somewhat  exceptional. 

It  will  take  but  a  moment's  reflectir  5  upon  the  part 


MODERN  CARPENTRY 


of  a  practical  man,  with  this  diagram  before  him,  to 
perceive  that  no  changes  are  necessary  in  the  rule 
where  the  span  is  more  or  less  than  24  feet.  The  cuts 
are  the  same  for  quarter  pitch  irrespective  of  the 
actual  dimensions  of  the  building.  The  square  in  all 
such  cases  is  used  on  the  basis  of  similar  triangles. 
The  broad  rule  is  simply  this:  To  construct  with  the 
square  such  a  triangle  as  will  proportionately  and  cor- 
rectly represent  the  full  size,  the  blade  becomes  the 
base,  the  tongue  the  altitude  or  rise,  while  the  hypoth- 

enuse  that  results  rep- 
resents the  rafter.  The 
necessary  cuts  are 
shown  by  the  tongue 
and  blade  respectively. 
In  order  to  give  a  gen- 
eral idea  of  the  use  of 
the  square  I  herewith  ap- 
pend a  few  illustrations 
of  its  application  in  framing  a  roof  of,  say,  one-third 
pitch,  which  will  be  supposed  to  consist  of  common 
rafters,  hips,  valleys,  jack  rafters  and  ridges.  Let  it 
be  assumed  that  the  building  to  be  dealt  with  measures 
30  feet  from  outside  to  outside  of  wall  plates;  the  toe 
of  the  rafters  to  be  fair  with  the  outside  of  the  wall 
plates,  the  pitch  being  one-third  (that  is  the  roof  rises 
from  the  top  of  the  wall  plate  to  the  top  of  the  ridge, 
one-third  of  the  width  of  the  building,  or  10  feet),  the 
half  width  of  the  building  being  15  feet.  Thus,  the 
figures  for  working  on  the  square  are  obtained;  if 
other  figures  are  used,  they  must  bear  the  same  relative 
proportion  to  each  other. 

To  get  the  required   lengths  of  the  stuff,   measure 
across  the  corner  of  the  square,  fruni  the  lo-inch  mark 


PRACTICAL  EXAMPLES 


83 


on   the   tongue    to  the  15-Inch   mark   on    the  blade, 
Fig.    29.     This  gives    18  feet  as   the   length   of   the 
common  rafter.      To  get  the  bottom  bevel  or  cut  to 
fit  on  the  wall  plate,  lay  the  square  flat  on  the  side  of 
the  rafter.     Start,  say,  at  the  right-hand  end,  with  the 
blade  of  the  square  to  the  right,  the  point  or  ant,'U;  of 
the  square  away  from  you,   and  the  rafter,   with  its 
back  (or  what  will  be  the  top  edge  of  it  when  it  is 
fixed)   towards  you.     Now  place  the  15-inch   mark  of 
the  blade  and  the  lo-inch  mark  of  the  tongue  on  the 
corner  of  the  rafter— that  is,  towards  you— still  keeping 
the   square   laid 
flat,    and    mark 
along   the  side  of 
the    blade.      This 
gives   the    bottom 
cut,    and    will    fit 
the   wall    plate. 
Now    move   the 
square  to  the  other 
end  of  the   rafter,    place   it   in   the  same   position   as 
before   to  the   18-foot  mark  on  the  rafter  and   to  the 
10-inch  mark  on  the  tongue,  and  the    15-inch  mark  on 
ihe  blade;     then  mark  alongside  the    tongue.      This 
gives  the  top  cut  to  fit  against  the  ridge.     To  get  the 
lens^rth  of  the  hip  rafter,  take    15  inches  on  the  blade 
and  15  inches  on  the  tongue  of  the  sqtiare,  and  measure 
across  the  corner.     This  gives  21^%  inches.     Now  take 
this  figure  on  the  blade  and  10  inches  on  the  tongue, 
then  measuring  across  the  corner  gives  the  length  of 
the  hip  rafter. 

Another  method  is  to  take  the  17-inch  mark  on  the 
blade  and  the  8-inch  mark  on  the  tongue  and  begin  as 
with  the  common   rafter,  as  at  Fig.  30.     Mark  along 


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84 


MODERN  CARPENTRY 


the  side  of  the  blade  for  the  bottom  cut.  Move  the 
square  to  the  left  as  many  times  as  there  are  feet  in 
the  half  of  the  width  of  the  building  (in  the  present 
case,  as  we  have  seen,  15  feet  is  half  the  width),  keep- 
ing the  above  mentioned  figures  17  and  8  in  line  with 

the  top  edge  of  the  hip  rafter; 
step  it  along  just  the  same  as 
when  applying  a  pitch  board  on 
a  stair-string,  and  after  moving 
it  along  15  steps,  mark  along- 
side the  tongue.  This  gives  the 
top  cut  or  bevel  and  the  length. 
The  reason  17  and  8  are  taken 
on  the  square  is  that  I2and  8  rep- 
resent the  rise  and  run  of  the 
common  rafter  to  i  foot  on  plan, 
while  17  and  8  correspond  with  the  plan  of  the  hips. 

To  get  the  length  of  the  jack  rafters,  proceed  in  the 
same  manner  as  for  common  or  hip  rafters;   or  alter- 
nately space  the  jacks  and  divide  the  length  of  the  com- 
mon rafter  into  the  same 
number  of  spaces.      This 
gives  the   length   of  each 
jack  rafter. 

To  get  the  bevel  of  the 
top  edge  of  the  jack  rafter, 
Fig.  31,  take  the  length, 
14^  of  the  common  rafter 

on  the  blade  and  the  run  of  the  common  rafter  on  the 
tongue,  apply  the  square  to  the  jack  rafter,  and  mark 
along  the  side  of  the  blade;  this  gives  the  bevel  or  cut. 
The  down  bevel  and  the  bevel  at  the  bottom  end  are 
the  same  as  for  the  common  rafter. 
To  get  the  bevel   for  the  side  of  the  purlin  to  fit 


PRACTICAL   EXAMPLES 


8S 


aj^^iinst  the  hip  rafter,  place  the  square  flat  against  the 
side  of  the  purlin,  with  8  inches  on  the  tongue  and 
143/8  inches  on  the  blade.  Fig.  32.  Mark  alongside  of 
the  tongue.  This  gives  the  side  cut  or  bevel.  The 
14^  inches  is  the  length  of  the  common  rafter  to  the 
l-foot  run,  and  the  8  inches  represent  the  rise. 

For  the  edge  bevel  of  puiiui,  lay  the  square  flat 
against  the  edge  of  purlin  with  12  inches  on  the  tongue 
and  141^  inches  on  the  blade,  as  at  Fig.  33,  and  mark 
along  the  side  of  the 
tongue.  This  gives 
the  bevel  or  cut  for  the 
edge  of  the  purlin. 

The  rafter  patterns 
must  be  cut  half  the 
thickness  of  ridge 
■shorter;  and  half  the 
thickness  of  the  hip  rafter  allowed  off  the  jack  rafters. 

These  examples  of  what  may  be  achieved  by  the  aid 
of  the  square  are  only  a  few  of  the  hundreds  that  can 
be  solved  by  an  intelligent  use  of  that  wonderful  instru- 
ment, but  it  is  impossible  in  a  work  of  this  kind  to 
illustrate  more  than  are  here  presented.  The  subject 
will  be  dealt  with  at  length  in  a  separate  volume. 


CHAPTER  II 


GENERAL  FRAMING  AND  ROOFING 

Heavy  framing  i.  now  almost  a  dead  science  in  this 
country  unless  it  be  in  the  far  west  or  south,  a&  steel 
and  iron  have  displaced  the  heavy  timber  structures 
that  thirty  or  forty  years  ago  were  so  plentiful  in 
roofs,   bridges  and   trestle-work.      As    it  will  not  be 


^u[ffiin|f][ljjl_jiij|iLr 


necessary  to  go  deeply  into  i.eavy-timber  framing, 
therefore  I  will  confine  myself  more  particularly  to  the 
framing  of  ballon  buildings  generally. 

A  ballon  frame  consists  chiefly  of  a  frame-work  of 
scantling.  The  scantling  may  be  2  x  4  inches,  or  any 
other  size  that  may  be  determined.  The  scantlings  are 
spiked  to  the  sills,  or  are  nailed  to  the  sides  of  the 
joist  which  rests  on  the  sills,  or,  as  is  sometimes  the 
case,    a    rough    floor    may  be    nailer!    on    the    joists 

36 


PRACTICAL   EXAMPLES 


87 


and  on  this,  ribbon  pieces 
of    2  X  4-inch     stuff     are 
spiked  around  to  the  outer 
edge    of    the    foundation, 
and    onto     these     ribbon 
pieces     the     scantling    is 
placed   and    "toe-nailed" 
to  them.     The  doors  and 
windows  are  spaced  off  as 
shown   in   Fig.   34,   which 
represents  a  ballon  frame 
and  roof    in    skeleton   condition.      These  frames   are 
generally  boarded  on  both  sides,  always  on  the  out- 
side     Sometimes  the  boarding  on  the  outside  is  nailed 
on    diagonally,    but    more 
frequeHtly      horizontally, 
which,    in  my  opinion,  is 
the  better  way,  providing 
always  the  boarding  is  dry 
and  the  joints   laid  close. 
The   joists   are    laid  on 
"rolling,"    that    is,    there 
are  no  gains  or  tenons  em- 
ployed, unless  in  trimmers 
or     similar     work.       The 
joists    are     simply    "toe- 
nailed" onto  sill  plates,  or 
ribbon  pieces,  as  shown  in  the  illustration.     Sometimes 
the  joists  are  made  to  rest  on  the  sills,  as  shown  in 

Fig.  35,  the  sill  being  no  more 

than  a  2  X  4-inch  scantling  laid 

in  mortar  on  the  foundation,  the 

—  >,^  outside  joists  forming  a  sill  for 

S-  37  the  side  studs.    A  better  plan  is 


.,o».3''«'"« 


W^^M^aW 


88 


MODERN   CARPENTRY 


shown  in  Fig.  36,  which  gives  a  met^'od  known  as  a 
"box-sill."  The  manner  of  construction  is  very 
simple. 


All  joists  in  a  building  of  this  kind  must  be  bridged 
similar  to  the  manner  shown  in  Fig.  37,  about  every 
eight  feet  of  their  length;  in  spans  less  than  sixteen 
feet,  nd  more  than  eight  feet,  a  row  of  bridging 
should  always  be  put  in  midway  in  the  span.  Bridg- 
ing should  not  be  less  than 
I  to  1^2  inches  in  section. 

In  trimming  around  a 
chimney  or  a  stair  weil-hole, 
several  methods  are  em- 
ployed. Sometimes  the 
headers  and  trimmers  are 
made  from  material  twice  as 
thick  and  the  same  depth  as 
the  ordinary  joists,  and  the  intermediate  joists  are 
tenoned  into  the  header,  as  showr  in  Fig.  38.  Here 
we  have  T,  T,  for  header,  and  T,  J,  T,  J,  for  trimmers, 
and  b,j,  for  the  ordinary  joists.  In  the  western,  and 
also  some  of  the  central  States,  the  trimmers  and 
headers  are  made  up  of  two  thicknesses,  the  header 
being  mortised  to  secure  the  ends  of  the  joists.     The 


PRACTICAL   liXAMPLES 


89 


two  thicknesses  are 
well  nailed  together. 
This  method  is  exhib- 
ited at  Fig.  39.,  which 
also  shows  one  way  to 
trim  around  a  hearth; 
C  shows  the  header 
with  trimmer  Joists 
with  tusk  tenons,  keyed 
solid  in  place. 

Frequently    it    hap- 
pens  that   a    chimney 
rises  in  a  building  from 
its  own  foundation,  disconnected 
from  the  walls,  in  which  case  the 
chimney  shaft  will  require  to  1: 
trimmed  all  around,  as  showh  .ii 


Fig.  42. 


-'^ 


Fig.  40.  In  cases  of 
th  J  kind  the  trim- 
mers A,  A,  should  be 
made  of  stuff  very 
much  thicker  than 
the  joists,  as  they 
have  to  bear  a  double 
burden;  B,  B  shovvs 
thj  heading,  and  C, 
C,  C,  C  the  tail  joists. 
E.  B,  should  have  a 
thickness  double  that 
of  C,  C,  etc.,  and  A, 
A  should  at  least  be 


90 


MODERN  CARPENTRY 


three  times  as  stout  as  C,  C.  This  will  to  some  extent 
equalize  the  strength  of  the  whole  floor,  which  is  a 
matter  to  be  considered  in  laying  down  floor  timbers, 
for  a  floor  is  no  stronger  than  its  weakest  part. 

There  are  a  number  of  devices  for  trimming  around 
stairs,  fire-places  and  chimney-stacks  by  which  the 
cutting  or  mortising  of  the  timbers  is  avoided.  One 
method  is  to  cut  the  timbers  the  exact  length,  square 

in  the  ends,  and  then  insert 
iron  dowels — two  or  more — 
in   the    ends    of    the   joists, 
and  then  bore  holes  in  the 
trimmers  and  headers  to  suit, 
and    drive   the   whole   solid 
together.      The   dowels   are 
made  from  J:^-inch  or  i-inch 
round  iron.     Another  and  a 
better  device  is  the  "bridle 
iron,"  which  may  be  hooked 
over  the  trimmer  or  header, 
as  the  case  may  be,  the  stir- 
rup carrying  the  abutting  timber,  as  shown  in  Fig.  41 
These      bridle    irons"    are  made   of    wrought    iron  — 
2  X  2Y2  inches,  or  larger  dimensions  if  the  work  require 
such;    for  ordinary  jobs,  however,  the  size  given  wiL 
be  found  plenty  heavy  for  carrying  the  tail  joists,  and  a 
little  heavier  may  be  employed  to  carry  the  header. 
This  style  of  connecting  the  trimmings  does  not  hold 
the  frame-work  together,  and  in  places  where  there  is 
any  tendency  to  thrust  the  work  apart,  some  provision 
must  be  made  to  prevent  the  work  from  spreading. 

In  trimming  for  a  chimney  in  a  roof,  the  "headers," 
"stretchers"  or  "trimmers,"  and  "tail  rafters,"  may 
be  simply  nailed  in  place,  as  there  is  no  great  weight 


PRACTICAL   EXAMPLES 


9« 


beyond  snow  and  wind  pressure  to  carry,  therefore 
the  same  precautions  for  strength  are  not  necessary. 
The  sketch  shown  at  Fig.  42  explains  how  the  chimney 
openint,^s  in  the  roof  may  be  trimmed,  the  parts  being 
only  spiked  together.  A  shows  a  hip  rafter  against 
which  the  cripples  on   both  sides  are  spiked.      The 

chimney-stack  is  shown  in  the  center  of  the  roof 

isolated— trimmed  on  the  four  sides.     The  sketch  is 


F«44. 


self-explanatory  in  a  measure,  and  should  be  easily 
understood. 

An  example  or  two  showing  how  the  rafters  may  be 
connected  with  the  plates  at  the  eaves  and  finished  for 
cornice  and  gutters,  may  not  be  out  of  place.  A  sim- 
ple method  is  shown  at  Fig.  43,  where  the  cornice  is 
complete  and  consists  of  a  few  members  only.  The 
gutter  is  attached  to  the  crown  moulding,  as  shown. 

Another  method  is  shown  at  Fig.  44,  this  one 
being  intended  for  a  brick  wall  having  sailing  courses 
over  cornice.     The  gutter  is  built  in  of  wood,  and  is 


9> 


MODERN  CARPENTRY 


lined  throughout  with  galvanized  iron  This  makes  a 
substantial  job  and  may  be  used  to  good  purpose  on 
brick  or  stone  warehouses,  factories  or  similar  build- 
in  cfs. 

Another   style  of   rafter   finish   is 
shown  at  Fig   45,  which  also  shows 
scheme   of   co/'nice.     A   similar   fin- 
ish   is   shown   at    Fig.  46,    the  cor- 
nice being   a  little  differ- 
ent.    In  both  the3'»  e>  im- 
ples,    the    gutters   are    of 
wood,    which     should    be 
lined   with  sheet  metal  of 
some  sort  in  order  to  pre- 
vent   their   t  o   rapio    de- 
cay.    At  Fig.  47  a  rafter 
finish    is    shown  which    n 
intended    for    a    veranda  or   porch. 
Here  the  construction  is  very  simple. 
The  rafters   are  dressed   and  cut  on 
projecting  end  to  represent  brackets 
and  form  a  finish 

From  these  examples  the  workman  ''1  ^et  sufficient 
ideas  for  working  his  rafters  to  suit  almost  any  condi- 
tion Though  there  are 
many  hundreds  of  styles 
which  might  be  presented, 
the  foregoing  are  ample 
for  our  purpose. 

It  will  now  be  in  order 
to  take  up  the   construc- 
tion of  roofs,  and  describe  the  methods  by  which  such 
construction  is  obtained. 
The  method  of  obtaining  the  lengths  and  bevels  of 


PRACTICAL   EXAMPLES 


93 


rafters  for  ordinary  roofs,  such  as  that  shown  in  Fig 
48,  has  already  been  given  in  the  chapter  on  the  steel 
square.  Something  has  also  bet^n  saiu  regarding  hip 
and  vall(  y  roofs;  but  not  enough,  I  think,  to  satisfy 
th..  full  requirements  of  ihe  workman,  so  I  will 
endeavor  to  give  a  clearer  idea  of  the  construction  of 
these  roofs  by  employing  the  graphic  system,  instead 
of  depending  altogether  on  the  steel  square,  though  I 


earnestly  advise  the  workman  to  "stick  to  the  square." 
It  never  makes  a  mistake,  though  the  owner  may  in  its 
application. 

A  "hip  rcof,"  pure  and  simple,  has  .10  gables,  and 
is  oftt:n  called  a  "cottage  nof,"  because  of  its  being 
best  adapted  for  cottages  ha.  ing  only  one,  or  one  and 
a  half,  stories.  The  chief  difficulty  in  its  construction 
is  getting  the  lengths  and  bevels  of  the  hip  or  angle 
rafter  and  the  jack  or  cripple  rafter.  To  the  expert 
workman,  this  is  an  easy  matter,  as  he  can  ieadily 
obtain  both  length?  and  bevels  by  aid  of  the  square,  or 
by  lines  such  as  I  am  about  to  produce. 


94 


MODERN  CARPENiRY 


w 


The  illustration  shown  at  Fig.  49  shows  the  simplest 
form  of  .»  hip  roof.  Here  the  four  hips  or  diagonal 
rafters  meet  in  the  center  of  the  plan.  Another  style 
of  hip  roof,  having  a  gable  and  a  ridge  in  the  center 

of  the  building,  is  shown  at 
Fig.  50.  This  is  quite  a 
common  style  of  roof,  and 
under  almost  every  condi- 
ig.  *\)t  **on  't  looks  well  and  has 

a  good  effect.     The  plan 
shows  lines  of  hips,  valleys  and  ridges. 

The  simplest  form  of  roof  is  that  known  as  the 
"lean-to"  roof.  This  is  formed  by  causing  one  side 
wall  to  be  raised  higher  than  the  opposite  side  wall,  so 
that  when  rafters  or 
joists  are  laid  from  the 
high  to  the  low  wall  a 
sloping  roof  is  the  re- 
sult. This  style  of  a 
roof  is  sometimes  called 
a  "shed  roof"  or  a 
"pent  roof."  The  shape 
is  shown  at  Fig.  51,  the 
upper  sketch  showing  i 
an  end  view  and  the  j 
lower  one  a  plan  of  the 
roof.  The  method  of 
framing  this  roof,  or 
adjusting    the     timbers 

It,  is  quite  obvious  and  needs  no  explanation. 
This  style  of  roof  is  in  general  use  where  an  annex  or 
shed  is  built  up  against  a  superior  building,  hence  its 
name  of  "lean-to,"  as  it  usually  "leans"  against  the 
main  building,  the  wall  of  which  is  utilized  for  the 


t^       ^  r- 


-'.JT^^j^^ 


'V\-  '■.,'■1 


PRACTICAL   EXAMPLES 


9S 


high  part  of  [ho  shed  or  annrx,  thiib  saving  the  co^t  of 
the  most  important  wall  of  the  structure. 

Next  to  the  "lean-to"  or  "shrcl  roof"  in  simplicity 
comes  the  "saddle"  or  "double  roof."  This  roof  ib 
shown  at  Fig.  52  by  the  end  view  on  the  top  of  the  fig- 
ure, and  the  plan  r  the  bottom.  It  will  be  seen  that 
this  roof  has  a  (  u^le  slope,  the  planes  forming  the 
slopes  are  equal'  .nclined  to  *he  horizor*  'Iic  meet- 
ing of  their  highest  sides  makes  an  -"  '-hich  is 
called  the  ridge  of  the  roof, 
and  the  triangular  spac<s  at 
the  end  of  the  walls  are 
called  gables. 

It  is  but  a  few  years  ago 
when  the  .nansard  roof  was 
very  popular,  and  many  of 
them  can  be  found  in  the 
older  parts  of  the  country, 
having  been  erected  be- 
tween the  early  fifties  and 
the  eight!  s,  but,  for  many 
fig.  51.  reasons,  t  ■  are  now  less 
used.  Fig.  53  si  ows  a  ,  jf  of  this  kind, 
trated  generally  l->y  tiormers,  as  shown  in  the  sketch, 
and  the  top  is  • -^vered  either  by  a  "deck  roof"  or  a 
very  h,  'nip  root,  is  shown.  Sometimes  the  sloping 
sitles  ot  these  roofs  are  curved,  which  give  them  a 
graceful  appearance,  but  add-  materially  to  their  cost. 
Another  style  of  roof  is  shown  at  Fig.  54.  This  is  a 
gambrel  roof,  and  was  very  much  in  evidence  in  pre- 
revolutionary  tunes,  particularly  among  our  Knicker- 
bocker ancestors.  In  conjunction  with  appropriate 
dormers,  this  style  of  roof  figures  prominently  in  what 
is   known   as   early   "colonial   style."      It   has   some 


Fig.  52, 
It  is  pene- 


MODERN  CARPENTRY 


advantages  over  the  mansard.  Besides  these  there  are 
many  other  kinds  of  roofs,  but  it  is  not  my  purpose  to 
enter  largely  into  the  matter  of  styles  of  roofs,  but 
simply  to  arm  the  workman  with  such  rules  and  prac- 
tical equipment  that  he 
will  be  able  to  tackle 
with  success  almost  anj' 
kind  of  a  roof  that  he 


maybe  called  upon  to 
construct. 

When  dealing  with 
the  steel  square  I  ex- 
plained how  the  lengths 
and  bevels  for  common  rafters  could  be  obtained  by 
the  use  of  the  steel  square  alone;  also  hips,  purlins, 
valleys  and  jack  rafters  might  be  obtained  by  the  use 
of  the  square,  but,  in  order  to  fully  equip  the  workman, 
I  deem  it  necessary  to  present  for  his  benefit  a  graphic 
method  of  obtaining  the  lengths,  cuts  and  backing  of 
rafters  and  purlins 
required  for  a  hip 
roof. 

At  Fig.  55,  I 
show  the  plans  of 
a  simple  hip  roof 
having  a  ridge. 
The  hips  on  the 
plan  form  an  angle  of  45^  or  a  miter,  as  it  were.  The 
plan  being  rectangular  leaves  the  ridge  the  length  of 
the  difference  between  the  length  and  the  width  of  the 
building.  Make  cd  on  the  ridge-line  as  shown,  half 
the  width  of  ab,  and  the  angle  bda  will  be  a  right  angle. 
Then  if  we  e.xtend  bd  to  c,  making  ^/<-  the  rise  of  the 
foof,  ae  will  be  the  length  of  the  hip  rafter,  and  the 


« 


PRACTICAL   EXAMPLES 


97 


angle  at  x  will  be  the  plumb  cut  at  point  of  hip  and 
the  angle  at  a  will  be  the  cut  at  the  foot  of  the  rafter. 
The  angle  at  v  shows  the  backing  of  the  hip.  This 
bevel  is  obtained  as  follows:  Make /t^  and  ah  equal 
distances — any  distance  will  serve— then  draw  a  line 
//^across  the  angle  of  the  building,  then  with  a  center 
on  ad  aX  p,  touching  the  line  ae  at  j,  describe  a  circle 
as  shown  by  the  dotted  line,  then  draw  the  lines  kh  and 


,^l  1 1 1 1  PTk 


kg^  and  that  angle,  as  shown  by  the  bevel  v,  will  be 
the  backing  or  bevel  for  the  top  of  the  hip,  beveling 
each  way  from  a  center  line  of  the  hip.  This  rule  for 
backing  a  hip  holds  good  in  all  kinds  of  hips,  also  for 
guttering  a  valley  rafter,  if  the  bevel  is  reversed.  A 
hip  roof  where  all  the  hips  abut  each  other  in  the  cen- 
ter is  shown  in  Fig.  56.  This  style  of  roof  is  generally 
called  a  "pyramidal  roof"  because  it  has  the  appear- 
ance of  a  low  flattened  pyramid.  The  same  rules 
governing  Fig.  55  apply  to  this  example.  The  bevels 
C  and  B  show  the  backing  of  the  hip,  B  showing  the 


98 


MODERN  CARPENTRY 


'4 


top  from  the  center  line 
ae\  and  C  showing  the 
bevel  as  placed  against 
the  side  of  the  hip,  which 
is  always  the  better  way 
to  work  the  hip.  A  por- 
tion of  the  hip  backed  is 
shown  at  C.  The  rise  of 
the  roof  is  shown  at  O. 

At  Fig.  57  a  plan  of  a 
roof  is  shown  where  the 
seats  of  the  hips  are  not 
on  an  angle  of  45°  and 
where  the  ends  and  sides 
of  the  roof  are  of  different 

pitches.     Take  the   base  line  of  the  hip,  ac  or  eg,  and 

make  ^perpendicular    to    ae,    from   ^,  and  equal    to 

the  rise  at/;  make  fa  ox  fg  for  the  length  of  the  hip, 

by  drawing  the  line  Im  at  right  angles  to  ae.     This 

gives  the  length  of  the  hip  rafter.     The  backing  of  the 

hip  is  obtained  in  a  like  manner  to  former  examples, 

only,  in  cases  of 

this    kind,    there 

are  two  bevels  for 

the  backing,  one 

side   of    the    hip 

being  more  acute 

than  the  other,  as 

shown  at   D  and 

E.      If    the    hips 

are  to  be  mitered, 

as    is    sometimes 

the  case  in  roofs 

of  this  kind,  then 


PRACTICAL  EXAMPLES 


99 


the  back  of  the  hip 
will  assume  the 
shape  as  shown  by 
the  two  bevels  at  F. 
A  hip  roof  having 
an  irregular  plan  is 
shown  at  Fig.  58. 
This  requires  no  ex- 
planation, as  the  hips  and  bevels  are  obtained  in  the 

same  manner  as  in  previous  examples.     The  backing 

of  the  hips  is  shown  at  FG. 

An  octagon  roof  is  shown  at  Fig.  59,  with  all  the 

lines  necessary  for  getting  the  lengths,  bevels,  and  back- 
ing for  the  hips. 

The    \i  n  e  ax 

shows  the    seat 

of   the    hip,   xe 

the  rise  of  roof, 

and    ae    the 

length   of    hip 

and  plumb  cut, 

and  the  bevel  at 

E   shows    the 

backing  of   the 

hips 

These    exam- 
ples  will    be 

quite    sufficient 

to    enable     the 

workman    to 

understand    the 

general     theory 

of     laying    out 

hip   roofs.      I 


lOO 


MODERN  CARPENTRY 


1^ 


1  ; 


may  also  state  that  to  save  a  repetition  of  drawing  and 
explaining  the  rules  that  govern  the  construction  of 
hip  roofs,  such  as  I  have  presented  serve  equally  well 
for  skylights  or  similar  work.  Indeed,  the  clever 
workman  will  find  hundreds  of  instances  in  his  work 
where  the  rules  given  will  prove  useful. 


"m^^lo^^l^M^ 


There  are  a  number  of  methods  for  getting  the 
lengths  and  bevels  for  purlins.  I  give  one  here  which 
I  think  is  equal  to  any  other,  and  perhaps  as  simple. 
Suppose  Fig.  60  -hows  one  end  of  a  hip  roof,  also  the 
rise  and  length  of  common  rafters.  Let  the  purlin  be  in 
any  place  on  the  rafter,  as  I,  and  in  its  most  com- 
mon position,  that  is,  standing  square  with  the  rafter; 
then  with  the  point  ^  as  a  center  with  any  radius, 
describe  a  circle.     Draw  two  lines,  ^/and  pn,  to  touch 


\: 


5^:  f 


PRACTICAL  EXAMPLES 


101 


the  circle/  and  q  parallel  \.o  fb  and  at  the  points  s  and 
r,  where  the  two  sides  of  the  purlin  intersect,  draw  two 
parallel  lines  to  the  forrT^r,  to  cut  the  diagonal  in  m 
and  k\  then  G  is  the  down  bevel  and  F  the  side  bevel 
of  the  purlin;  these  t.vo  bevels,  when  applied  to  the 
end  of  the  purlin,  and  when  cut  by  them,  will  exactly 
fit  the  side  of  the  hip  rafters. 

To  find  the  cuts  of  a  purlin  where  two  sides  are 
parallel  to  horizon:  The  square  at  B  and  the  bevel  at 
C  will  show  how  to  draw  the  end  of  the  purlin  in  this 
easy  case.  Th  following  is  universal  in  all  posi- 
tions of  the  pur.a:  Let  <?(^  be  the  width  of  a  square 
roof,  make  bfox  ae  one-half  of  the  width,  and  make  cd 
perpendicular  in  the  middle  of  ef,  the  height  of  the 
roof  or  ri'.e,  which  in  this  case  is  one-third;  then  draw 
de  and  df,  which  are  each  the  length  of  the  common 
rafter. 

To  find  the  bevel  of  a  jack  rafter  against  the  hip, 
proceed  as  follows:  Turn  the  stock  of  the  side  bevel 
at  F  from  a  around  to  the  line  ?>,  which  will  give  the 
side  bevel  of  the  jack  rafter  The  bevel  at  A,  which  .« 
the  iop  of  the  common  rafter,  is  the  down  bevel  of  the 
jack  rafter. 

At  D  the  method  of  getting  the  backing  of  a  hip 
rafter  is  shown  the  same  as  explained  in  other  figures. 

There  are  other  methods  of  obtaining  bevels  for 
purlins,  but  the  one  offered  h-^re  will  suffice  for  all 
practical  purposes. 

1  gc've  a  method  of  finding  the  back  cu  or  jack 
rafter!  by  the  steel  square,  in  a  previous  ciicipter.  I 
give  another  rule  herewith  for  the  steel  square:  Take 
the  length  of  the  common  rafter  on  the  blade  and  the 
run  of  the  same  rafter  on  the  tongue,  and  the  blade  of 
the  square  will  give  the  bevel  for  the  cut  on  the  back 


W^ 


toa 


MODERN   CARPENTRY 


of  the  jack  rafter.  For  example,  suppos':  the  rise  to 
be  6  feet  and  the  run  8  feet,  the  leng'.h  of  the  _ommon 
rafter  will  be  lo  feet.  Then  take  lO  fi  ct  on  the  blade 
of  he  square,  and  8  feet  on  the  tonjrue,  and  the  blade 
will  give  the  back  bevel  for  the  cut  of  the  jack 
rafters. 

To  obtain  the  length  of  jack  rafters  is  a  ver^'  simple 
process,  and  may  be  obtained  easily  by  a  diagram,  as 
shown  in  Fig.  6l,  which  is  a  very  common  method: 

First  lay  off  half  the  width 
of  the  building  to  scale,  as 
from  A  to  B,  the  length  of 
the  common  rafter  B  to  C, 
and  the  length  of  the  hip 
rafter  from  A  to  C.  Space 
off  the  widths  from  jack 
rafter  to  jack  rafter  as  shown 
by  the  lines  I,  2,  3,  and 
measure  them  accurately. 
Then  the  lines  i,  2,  and  3 
will  be  the  exact  lengths  of 
the  jack  rafters  in  those  divisions.  Any  number  of 
jack  rafters  may  be  laid  off  this  way,  and  the  result 
will  be  the  length  of  each  rafter,  no  matter  whc  may 
be  the  pi*ch  of  the  roof  or  the  distance  the  rafters  are 
apart. 

A  table  for  determining  the  length  of  jack  rafters  is 
given  below,   which  shows   the    lengths  required    for 
different  spacing  in  three  pitches: 
One-quarter  pitch  roof: 

They  cut  13.5  inches  shorter  each  time  when  spaced 
12  inches. 

They  cut  18  inches  shorter  each  time  when  spaced 
16  inches. 


PRACTICAL  EXAMPLES 


103 


They  cut  27  inches  shorter  each  time  when  spaced  24 
inches. 

One-third  pitch  roof: 

They  cut  14.4  inches  shorter  each  time  when  spaced 
12  inches. 

They  cut  19.2  inches  shorter  each  time  when  spaced 
16  inches. 

They  cut  28.8  inches  shorter  each  time  when  spaced 
24  inchcj. 

One-half  pitch  roof; 
"  They  cut  17  inches  shorter  each  time  when  spaced 
J2  inches. 


They  cut  22.6  inches  shorter  each  time  when  spaced 
16  inches. 

They  cut  34  inches  shorter  each  time  when  spaced 
24  inches. 

It  is  not  my  intention  to  enter  deeply  into  a  discus- 
sion of  the  proper  methods  of  constructing  roofs  of  all 
shapes,  though  a  few  hints  and  diagrams  of  octagonal, 
domical  and  other  roofs  and  spires  will  dou'jtless  be 
of  service  to  ihe  general  workman.  One  of  the  most 
useful  methods  of  trussing  a  roof  is  that  known  as  a 
lattice  "built-up"  truss  roof,  similar  to  that  shown  at 
Fig.  62.  The  rafters,  tie  beams  and  the  two  main 
braces  A,  A,  must  be  of  one  thickness — say.  2  x  4  or 
2x6  inches,  according  to  the  length  of  the  span — 
while  the  mine  *»"Aces  are  made  of  i-inch  stuff  and 


104 


MODERN   CARPENTRY 


about  10  or  12  inches  wide.  These  minor  braces  are 
well  nailed  to  the  tie  beams,  main  braces  and  rafters. 
The  main  braces  must  be  halved  over  each  other  at 
their  juncture,  and  bolted.  Sometimes  the  main 
braces  are  left  only  half  the  thickness  of  the  rafters, 
then  no  halving  will  be  necessary,  but  this  method  has 
the  disadvantage  of  having  the  minor  braces  nailed  to 
one  side  only.  To  obviate  this,  blocks  maybe  nailed  to 
the  inside  of  the  main  braces  to  make  up  the  thickness 


required,  as  shown,  and  the  minor  braces  can  be  nailed 
oj  bolted  to  the  main  brace. 

The  rafters  and  tie  beams  are  held  together  at  the 
foot  of  the  rafter  by  an  iron  bolt,  the  rafter  having  a 
crow-foot  joint  at  the  bottom,  which  is  let  into  the  tie 
beam.  The  main  braces  also  are  framed  into  the 
rafter  with  a  square  toe-joint  and  held  in  place  with 
an  iron  bolt,  and  the  foot  of  the  brace  is  crow-footed 
into  the  tic  beam  over  the  wall. 

This  truss  is  easily  made,  maybe  put  together  on 
the  ground,  and,  as  it  is  light,  may  be  hoisted  in  place 
with  blocks  and  tackle,  with  but  little  trouble.  This 
truss  can  be  made  sufficiently  strong  to  span  a  roof 
from  40  to  75  feet.     Where  the  span  inclines  to  the 


PRACTICAL  EXAMPLES 


greater  length,  the 
tic  beams  and  raft- 
ers may  be  made  of 
built-up  timbers,  but 
in  such  a  case  the 
tie  beams  should 
not  be  less  than 
6  X  10  inches,  nor 
the  rafters  less  than 
6x6  inches. 

Another  style  of 
roof  altoi^ether  is 
shown  at  Fig.  63. 
This  is  a  self-sup- 
porting roof,  but  is 
somewhat  expensive 
if  intended  for  a 
building  having  a 
span  of  30  feet  or 
less.  If:  is  fairly 
well  adapted  for 
halls  or  for  country 
churches,  where  a 
high  ceiling  is  re- 
quired and  the  span 
anywhere  from  30 
to  50  feet  over  all. 
It  would  not  be  safe 
to  risk  a  roof  of  this 
kind  on  a  building 
having  a  span  more 
than  50  feet.  The 
main  features  of  this 
roof  are:    (i)  having 


io6 


MODERN   CARPENTRY 


:!'i 


collar  beams,  (2)  truss  bolts,  and  (3)  iron  straps  at  the 
joints  and  triple  bolts  at  the  feet. 

I  show  a  dome  and  the  manner  of  its  construction  at 
Fig.  64.  This  is  a  fine  example  of  French  timber 
framing.  The  main  carlins  are  shown  at  <7,  b,  c,  d 
and  e,  Nos.  i  and  2,  and  the  horizontal  ribs  are  also 
shown  in  the  same  numbers,  with  the  curve  of  the 
outer  edge  described  on  them.  These  ribs  are  cut  in 
between  the  carlins  or  rafters  and  beveled  0.''  to  suit. 
This  dome  may  be  boarded  over  either  horizontally  or 
with  boards  made  into  "gores"  and 
laid  on  in  line  with  the  rafters  or 
carlins. 

The  manner  of  framing  is  well 
illustrated  in  Nos.  3  and  4  in  two 
ways.  No.  3  being  intended  to  form 
the  two  principal  trusses  which 
stretch  over  the  whole  diameter, 
while  No.  4  may  be  built  in  between 
the  main  trusses. 

The  illustrations  are  simple  and 
clear,  and  quite  sufficient  without 
further  explanation. 
Fig.  65  exiiibits  a  portion  of  the  dome  of  St.  Paul's 
Cathedral,  London,  which  was  designed  by  Sir  Chris- 
topher Wren  The  system  of  the  framing  of  the 
external  dome  of  this  roof  is  given.  The  internal 
cupola,  AAl,  is  of  brick-work,  two  bricks  in  thickness, 
with  a  course  of  bricks  18  inches  in  length  at  every  five 
feet  of  rise.  These  serve  as  a  firm  bond.  This  dome 
was  turned  upon  a  wooden  center,  whose  only  support 
was  the  projections  at  the  springing  of  the  dome, 
which  is  said  to  have  been  unique.  Outside  the  brick 
cupola,   which   is  only  alluded    to  in  order  that   the 


PRACTICAL  EXAMPLES 


107 


description  may  be  the  more  intelligible,  rises  a  brick* 
work  cone  B.  A  portion  of  this  can  be  seen,  by  a 
spectator  on  the  floor  of  the  cathedral,  through  the 
central  opening  at  A.  The  timbers  which  carry  the 
externa!  dome  rest  '.pon  this  conical  brickwork.  The 
horizontal  hammer  beams,  C,  D,  E,  F,  are  curiously 
tied  to  the  corbels,  G,  H,  I,  K,  by  iron  cramps,  well 
^  bedded  with  lead  into  the 
corbels  and  bolted  to  the  ham- 
mer beams.  The  stairs,  or  lad- 
ders, by  which  the  ascent  to  the 
Golden  Gallery  or  the  summit 


Fig.  66. 


of  the  dome  is  made,  pass  among  the  roof  trusses. 
The  dome  has  a  planking  from  the  base  upwards,  and 
hence  the  principals  are  secured  horizontally  at  a  little 
distance  from  each  other.  The  contour  of  this  roof  is 
that  of  a  pointed  dome  or  arch,  the  principals  being 
segments  of  circles;  but  the  central  opening  for  the 
lantern,  of  course,  hinders  these  arches  from  meeting 
at  a  point.  The  scantling  of  the  curved  principals  is 
10  X  ll}4  inches  at  the  base,  decreasing  to  6  x  6  inches 


io8 


MOI    AN  CARPENTRY 


II 


J 


at  thf  top.  A  lantern  of  Portland  ston  crowns  the 
summit  of  the  dome.  The  method  of  framing  will  be 
clearly  seen  in  the  diagram.  It  is  in  every  respect  an 
excellent  specimen  of  roof  construction,  and  is  worthy 
of  the  genius  and  mathematical  skill  of  a  great  work- 
man. 

With  the  rules  offered  herewith  for  the  construction 
of  an  octagonal  spire,  I  close  the  subject 
of  roofs:  To  obtain  bevels  and  lengths  of 
braces  for  an  octagonal  spire,  or  for  a 
spire  of  any  number  of  sides,  let  AB, 
Fig.  66,  be  one  of  the  sides.  Let  AC  and 
BC  be  the  seat  line  of  hip.  Let  AN  be 
the  seat  of  brace.  Now,  to  find  the  posi- 
tion of  the  tie  beam  on  the  hips  so  as  to 
be  square  with  the  boardinr.  draw  a  line 
through  C,  square  with  AB,  indefinitely. 
From  C,  and  square  with  EC,  draw  CM, 
making  it  equal  to  the  height.  Join  EM. 
.-:,       X    .     Let  OF  be  the  height  of  the  tic  beam. 

Il  FiffcW  ^^  ^  ^^^  '  ^^"^""^  ^'^*^  E^^  ^  ''"^»  which 
^       ■  '"^'    produce  until  it  cuts  EC  prolonged  at  G. 

Draw  CL  square  with  BC.  Make  CL  in 
length  equal  to  EM.  Join  BL,  and  make  NH  equal  to 
OF.  From  G  draw  the  line  GS  parallel  with  AB,  cut- 
ting BC  prolonged,  at  the  point  S;  then  the  angle  at  H 
is  the  bevel  on  the  hip  for  the  tie  beam.  For  a  bevel 
to  miter  the  tie  beam,  make  FV  equal  ON.  Join  VX; 
then  the  bevel  at  V  is  the  bevel  on  the  face.  For  the 
down  bevel  see  V,  in  Fig.  67.  To  find  the  length  of 
brace,  make  AB,  Fig.  67.  equal  to  AB,  Fig.  66.  Make 
AL  and  BL  equal  to  BL,  Fig.  66.  Make  BP  equal  to 
BH.  Join  AP  and  BC,  which  will  be  the  length  of  the 
brace.     The  bevels  numbered  i,  3,  5  and  7  are  all  to  be 


PRACTICAL   EXAMPLES 


109 


used,  as  shown  on  the  edge  of  the  brace.  No.  I  is  to 
be  used  at  the  top  above  No.  5.  For  the  bevel  on  the 
face  to  miter  on  the  hip,  draw  AG,  Fig.  66,  cutting  BS 
at  J.  Join  JH.  Next,  in  Fig.  68,  make  A'  ^qual  AP, 
Fig.  67,  and  make  AJ  equal  to  AJ,  Fig.  66.  Make 
rj  equal  to  J! I,  Fig.  66,  and  make  PI  equal  to  HI. 
Join  AI;  then  the  bevel  marked  No.  5  will  be  correct 
for  the  beam  iiext  to  the  hip,  and  the  bevel  marked 
No.  6  will  be  correct  for  the  top.  Bevel  No.  2  in  this 
figure  will  be  correct  for  the  beam  next  to  the  plate. 
The  edge  of  the  brace  is  to  correspond  with  the 
boarding. 

A  few  examples  of  scarfing  tim- 
ber are  presented  at  Figs.  69,  70,  71 
and  "jz.  The  example  shown  at 
Fig.  69  exhibits  a  mechod  by 
which  the  two  ends  of  the  timber 
arc  joined  together  with  a  step- 
splice  and  spur  or  tenon  on  end,  it 
being  drawn  tight  together  by  the 
keys,  as  shown  in  th  j  shaded  part.  Fig.  70  is  a  similar 
joint  though  simpler,  -^nd  therefore  a  better  one;  A,  A 
are  generally  joggle  A  hardwood,  and  not  wedged 
keys,  but  the  latter  are  preferable,  as  they  allow  of 
tightening  up.  TIic  shearing  used  along  BF  should  be 
pine,  and  be  not  less  than  six  and  a  half  times  BC; 
and  BC  shou'd  be  equal  to  at  least  twice  the  depth  of 
the  key.  The  shear  in  the  keys  being  at  right  angles 
to  the  grain  of  the  wood,  a  greater  stress  per  square 
inch  of  shearing  area  can  be  put  upon  them  than 
along  BF,  but  their  shearing  area  should  be  equal  in 
strength  to  the  othei  parts  of  the  joint;  oak  is  the 
best  word  for  thcui,  as  its  shearing  is  from  four  to  five 
times  that  of  pine. 


no 


MODERN   CARPENTRY 


m 


:     I 


Scarfed  joints  with  bolts  and  indents,  such  as  that 
shown  at  Fig.  71,  are  about  the  strongest  of  the  kind. 
From  this  it  will  be  seen  that  the  strongest  and  most 
economical  method  in  every  way,  in  lengthening  ties, 
is  by  adoption  of  the  common  scarf  joint,  as  shown  at 
Fig.  71,  and  finishing  the  scarf  as  there  represented. 

The  carpenter  meets  with  many  conditions  when 
timbers  of  various  kinds  have  to  be  lengthened  out 


"ri£'.65 


rs 


D 


tti 


u 


iu- 


? 


Fiff.  70.' 


^ig.  72. 


t^        wW 


and  spliced,  as  in  the  case  of  wail  plates,  etc.,  where 
there  is  not  much  tensile  stress.  In  such  cases  the 
timbers  may  simply  be  halved  together  and  secured 
with  nails,  spikes,  bolts,  screws  or  pins,  or  they  may 


PRACTICAL  EXAMPLES 


lit 


be  halved  or  beveled  as  shown  in  Fig.  72,  which,  when 
boarded  above,  as  in  the  case  of  wall  plates  built  in 
the  wall,  or  as  stringers  on  which  partitions  are  set,  or 
joint  beams  on  which  the  lower  edges  of  the  joists  rest, 
will  hold  good  together. 

Treadgold  gives  the  following  rules,  based  upon  the 
relative  resistance  to  tension,  crushing  and  shearing 
of  different  woods,  for  the  proportion  which  the  length 
or  overlap  of  a  scarf  should  bear  to  the  depth  of  the 
tie: 


without 
bolis 

6 


With 
bolU 


3 
6 


With  bolts 
and  indents 

2 


Oak,  ash,  elm,  etc.    . 

Pine  and  similar  woods  .     12  o  4 

There  are  many  other  kinds  of  scarfs  that  will  occur 

to  the  workman,  but  it  is  thought  the  foregoing  may 

be  found  useful  on  special 


li 


occasions. 

A  few  examples  of  odd 
joints  in  timber  work  will 
not  be  out  of  place.  It 
sometimes  happens  that 
cross-beams  are  required 
to  be  fitted  in  between 
girders   in   position,  as   in 

renewing  a  defective  one,   and  when  this  has 
done,  and  a  mortise  and  tenon  joint  is  used,  a 


Fig.,73.! 


M\ 


to  be 
chase 

has  to  be  cut  leading  into  the  mortise,  as  shown  in  the 
horizontal  section.  Fig.  73.  By  inserting  the  tenon  at 
the  other  end  of  the  beams  into  a  mortise  cut  so  as  to 
allow  of  fitting  it  in  at  an  angle,  the  tenon  can  be  slid 
along  the  chase  d  into  its  proper  position.  It  is  better 
in  this  case  to  dispense  with  the  long  tenon,  and,  if 
necessary,  to  substitute  a  bolt,  as  shown  in  the  sketch. 
A  mortise  of  this  kind  is  called  a  chase  mortise,  but  an 


112 


MODERN  CARPENTRY 


m 


i 


w^ 


Fig  74. 


fe 


^WA 


iron  shoe  made  fast  to  the  girder  forms  a  better  means 
of  carrying  the  end  of  a  cross-beam.  The  beams  can 
be  secured  to  the  shoe  with  bolts  or  other  fastenings. 
To  support  the  end  of  a  horizontal  beam  or  girt  on 
tjie  side  of  a  post,  the  joint  shown  in  Fig.  74  may  be 

used  where  the  mortise  for 
the  long  tenon  is  placed,  to 
weaken  the  post  as  little  as 
possible,  and  the  tenon  made 
about  one-third  the  thickness 
of  the  beam  on  which  it  is  cut. 
The  amount  of  bearing  the 
beam  has  on  the  post  must 
greatly  depend  on  the  work  it 
has  to  do.  A  hardwood  pin 
can  be  passed  through  the 
cheeks  of  the  mortise  and  the  tenon  as  shown  to  keep 
the  latter  in  position,  the  holes  being  draw-bored  n\ 
order  to  bring  the  shoulders  of  the  tenon  tight  home 
against  the  post,  but  care  must  be  taken  not  to  overdo 
the  draw-boring  or  the  wood  at  the  end  of  the  tenon 
will  be  forced  out  by  the 
pin.  The  usual  rule  for 
draw-boring  is  to  allow  a 
quarter  of  an  inch  draw  in 
soft  woods  and  one-eighth 
of  an  inch  for  hard  woods. 
These  allowances  may  seem  rather  large,  but  it  must 
be  remembered  that  both  holes  in  tenon  and  mortise 
will  give  a  little,  so  also  will  the  draw  pin  itself  unless 
it  is  of  iron,  an  uncommon  circumstance. 

Instead  of  a  mortise  and  tenon,  an  iron  strap  or  a 
screw  bolt  or  nut  may  be  used,  similiar  to  that  shown 
in  Fig.  75. 


[se*Vi5,*iiS'pj„  ,_ 


m 


PRACTICAL  EXAMPLES 


113 


1 


/M 


The  end  of  the  beam  may  also  be  supported  on  a 
block  which  should  be  of  hardwood,  spiked  or  bolted 
^  on  to  the  side  of  the 

•At*!  post,  as  at  A  and  B, 

Fig.  76.  The  end  of 
the  beam  may  either 
be  tenoned  into  the 
post  as  shown,  or  it 
may  have  a  shoulder, 
with  the  end  of  the 
beam  beveled,  as 
shown  at  A. 

Heavy  roof  tim- 
bers are  rapidly  giv- 
ing place  to  steel,  but 
there  yet  remain 
many  cases  where 
timbers  will  remain  employed  and  the  old  method  of 
framing  continued.  The  use  of  iron  straps  and  bolts 
in  fastening  timbers  together  or  for  trussing  purposes 
will  never  perhaps  become  obsolete,  therefore  a  knowl- 
edge of  the  proper  use  of 
these  will  always  rei-,:  n 
valuable. 

Heel  straps  are  used  to 
secure  the  joints  between 
inclined  struts  and  hori- 
zontal beams,  such  as  the 
joints  between  rafters  and 
beams.  They  may  be  placed  either  so  as  merely  to 
hold  the  beams  close  together  at  the  joints,  as  in  Fig. 
"JT,  or  so  as  to  directly  resist  the  thrust  of  the  inclined 
strut  and  prevent  it  from  shearing  off  the  portion  of 
the  horizontal  beam  against  which  it  presses.     Str?ps 


u 


tl4 


MODERN  CARPENTRY 


P 


of  the  former  kind  are  sometimes  called  kicking-straps. 
The  example  shown  at  Fig.  yj  is  a  good  form  of  strap 
for  holding  a  principal  rafter  down  at  the  foot  of  the 
tie  beam.  The  screws  and  nuts  are  prevented  from 
sinking  into  the  wood  by  the  bearing  plate  B,  which 
acts  as  a  washer  on  which  the  nuts  r'de  when  tighten- 
ing is  done.  A  check  plate  is  also  provided  under- 
neath to  prevent 
the  strap  cutting 
into  the  tie  beam. 
At  Fig.  78  I  show 
a  form  of  joint 
often  used,  but  it 
repress  its  a  diffi- 
culty in  getting 
the  two  parallel 
abutments  to  take 
their  fair  share  of 
the  work,  both 
from  want  of  accu- 
racy in  workman- 
ship as  we!'  as 
from  the  disturb- 
ing influence  of 
shrinkage.  In 
making  a  joint  of  this  sort,  care  must  be  taken  that 
sufficient  wood  is  left  between  the  abutments  and  the 
end  of  the  tie  beam  to  prevent  shearing.  A  little 
judgment  in  using  straps  will  often  save  both  time 
and  money  and  yet  be  sufficient  for  all  purposes. 

I  show  a  few  examples  of  strengthening  and  trussing 
joints,  girders,  and  timbers  at  Fig  79.     The  diagrams 
need  no  explanation,  as  they  are  splf-evident. 
It  would  expand  this  book  far  beyond  the  dimensions 


PRACTICAL   EXAMPLES 


"5 


awarded  me,  to  even  touch  on  all  matter:^  pertaining 
to  carpentry,  including  bridges,  trestle?,  trussed  gird- 
ers and   trusses  generally,  so   I   must  content   mvself 


W  \r''^^^^^^ 


■^ 


•^r^ 


^^sx 


with  wha«       s  already  been  given  or  -.ne  subject  of 
carpentr\  ough,  as  the  reader  is  aware,  the  subject 

is  only  sun     cd. 


:ii 


iii 


f1 


PART  III 


JOINER'S  WORK 


\ 


CHAPTER   I 

KERFINC,    RAKING    MOULDINGS,    HOPPERS   AND   SPLAYS 

This  department  could  be  extended  indefinitely,  as 
the  problems  in  joinery  are  much  more  numerous  than 
in  carpentry,  but  as  the  limits  of  this  book  will  not 
permit  me  to  cover  the  whole  range  of  the  art,  even  if 

I  were  competent,   I 
must    be    contented 
with    dealing    with 
/  those    problems    the 

fij-  1.        /'  workman    will    most 

^^  likely  be  confronted 

-X     with  in  his  daily  oc- 
cupation. 

First  of  all,  I  give  several  methods  of  "keriing,"  for 
few  things  puzzle  the  novice  more  than  this  litlie 
problem.  Let  us  suppose  any  circle  around  which  it 
IS  desired  to  bend  a  piece  of  stuff  to  be  2  inches  larger 
on  the  outside  than  on  the  inside,  or  in  other  words, 
the  veneer  is  to  be  i  inch  thick,  then  take  out  as  many 
saw  kerfs  as  will  measure  2  inches.  Thus,  if  a  saw 
cuts  a  kerf  one  thiity-second  of  an  inch  in  width,  then 
it  will  take  64  kerfs  :n  the  half  circle  to  allow  for  the 

"7 


i^*^ 


H 


ii8 


MODERN  CARPENTRY 


veneer  to  bend  around  neatly.  The  piece  being 
placed  in  position  and  bent,  the  kerfs  will  exactly 
close. 

Another  way  is  to  saw  one  kerf  near  the  center  of 
the  piece  to  be  bent,  then  place  it  on 
the  plan  of  the  frame,  as  indicated  in  the 
sketch  and  bend  it  until  the  kerf  closes. 
The  distance,  DC,  Fig.  I,  on  the  line  DB, 
will  be  the  space  between  the  kerfs  neceS' 
sary  to  complete  the  bending. 

In  kerfing  the  workman  should  be  care- 
ful to  use  the  same  saw  throughout,  and  to 
cut  exactly  the  same  depth  every  time,  and 
the  spaces  must  be  of  equal  distance.  In 
diagram  Fig.  i,  DA  shows  the  piece  to 
be  bent,  ami  at  O  the  thickness  of  the 
stuff  is  shown,  also  path  of  the  inside  and 
outside  of  the  circle. 

Another,  and  a  safe  method  of  kerfing 

is  shown  at  Fig. 
2,  in  which  it  is 
desired  to  bend 
a  piece  as 
shown,  a  n  d 
which  is  in- 
tended to  be 
secured  at  the 
ends.  Up  to  A 
is  the  piece  to 
be  t  r  e  a  t  e  tl  . 
First  gauge  a  line  on  about  one-eighth  inch  back  from 
the  face  edges,  and  try  how  far  it  will  yield  when  the 
first  cut  is  made  up  to  the  gauge  line,  being  cut  perleclly 
straight  through  from  side  to  side,  then  place  the  work 


JOINER'S  WORK 


119 


»t 


r 


on  a  flat  board  and  try  it  pontly  until  the  kerf  closes, 
and  it  goes  as  far  as  is  shown  at  A,  which  is  the  first 
cut,  R  rcprcsentinjT  the  second.  Those  are  the  dis- 
tances the  kerfs  require  to  be  placed  apart  to  complete 
the  curve.  Try  the  work  :■<  it  progresses.  This  eases 
the  back  of  it  and  makes  ■  much  easier  done  when  the 
whole  cuts  arc  finished.  Now  make  certain  that  the 
job  will  fold  to  the  curve,  th.  n  fill  them  all  with  hot 
glue  and  proceed  to  fix.  The  plan  shown  here  is  a 
half  semi,  and 
may  be  in  excess 
of  what  is  wanted, 
but  the  principle 
holds  good. 

Another  method 
is  shown  at  Fig.  3 
for  determining 
the     number    and 

distances  apart  of  the  saw  kerfs  required  to  bend  a 
board  round  a  corner.  The  board  is  first  drawn  in 
position  and  a  half  of  it  divided  into  any  rumber  of 
equal  parts  by  radii,  as  I,  2,  3,  4,  5,  6.'  A  straight 
piece  is  then  marked  off  to  correspond  with  the  divi- 
sions on  the  circular  one.  By  this  it  is  seen  that  the 
part  XX  must  be  cut  away  by  saw  kerfs  in  order  to  let 
the  board  turn  round.  It  therefore  depends  upon  the 
thickness  of  the  saw  for  the  number  of  kerfs,  and  when 
that  is  known  the  distances  apart  can  be  determined  as 
shown  on  the  right  in  the  figure.  Here  eight  kerfs  are 
assumed  to  be  requisite. 

To  make  a  kerf  for  bending  round  an  ellipse,  such  as 
that  shown  at  Fig.  4,  proceed  as  shown,  CC  and  GO 
being  the  distances  for  the  kerfs;  2  to  2  and  2  103  are  the 
lengths  of  the  points  EF,  w^hile  BB  is  the  length  of  the 


Ipt 


I30 


MODERN  CARPENTRY 


points  EE,  making  the  whole  head  piece  in  one.     In 
case  it  is  necessary  to  joint  D,  leave  the  ends  about 
inches  longer  than  is  necessary,  as  shown   by  N  in  the 


IZS 


sketch,   so   that   should   a  breakage  occur  this  extra 
length  may  be  utilized. 

It  is  sometimes  necessary  to  bend  thick  stuff  around 
work  that  is  on  a  rake,  and  when  th  s  is  required,  all 
that  is  necessary  is  to  run  in  the  kerfs  the  angle  of  the 
rake  whatever  that  may  be,  as 
shown  at  Fig.  5.  This  rule  holds 
good  for  all  pitches  or  rakes. 
Fig.  6  shows  a  very  common 
way  of  obtaining  the  distance 
to  place  the  kerfs.  The  piece 
to  be  kerfed  is  shown  at  C; 
now  make  one  at  E;  hold  firm 
the  lower  part  of  C  and  bend  pi^g^  ^^ 


n 


JOINER'S  WORK 


iti 


the  upper  end  on  the  circle  F  until  the  kerf  is  closed. 
The  line  started  at  E  and  cutting  the  circumference  of 
the  circle  indicates  at  the  circumference  the  distance 
the  saw  kerfs  will  be  apart.  Set  the  dividers  to  this 
space,  and  be- 
ginning at  the 
center  cut, 
space  the  piece 
to  be  kerfed 
both  ways. 
Use  the  same 
saw  in  a'l  cuts 
and  let  it  be 
clean  and  keen, 
with  all  dust 
well  cleaned 
out. 

To    miter 
mouldings, 

where  straight  lines  must  merge  into  lines  having  a 
curvature  as  in  Figs.  7  and  8:  In  all  cases,  where  a 
straij^ht  moulding  is  intersected  with  a  curved  mould- 
ing,' of  the  same  profile  at  whatever  angle,  the  miter  is 
♦necessarily  other  than  a  straight  line.     The  miter  line 

is  found  by  the  intersec- 
tion of  lines  from  the 
several  points  of  the  pro- 
file as  they  occur  respect- 
ively in  the  straight  and 
the  curved  mouldings. 
In  order  to  find  the  miter 
between  two  such  mould- 
.  ,  in;Ts  first  project  lines 
'. }^    from  all  of  the  poir.*^?  of 


laa 


MODERN   CARPENTRY 


•m< 


the  profile  indefinitely  to  the  right,  a«  shown  in  the 
elevation  of  the  sketch.  Now.  upon  the  center  line  of 
the  curved  portion,  or  un.^n  any  line  radiating  from 
the  c<nter  around  which  the  curved  moulding  is  to  be 

carried,  set  off  the 
several  points  of 
the  profile,  spac- 
ing them  exactly 
the  same  as  they 
are  in  the  eleva- 
tion of  the  straight 
moulding.  Place 
one  leg  of  the 
dividers  at  the 
center  of  the  cir- 
cle, bringing  the  other  leg  to  each  of  the  several  points 
upon  the  curved  moulding,  and  carry  lines  around  the 
curve,  intersecting  each  with  a  horizontal  line  from 
the  corresponding  point  of  the  level  moulding.  The 
dotted  line  drawn  th-  t|(rh  th;-  intersections  at  the 
miter  shows  what 
must  be  the  real 
miter  line. 

Another  odd  miter- 
ing  of  this  class  is 
shown  ill  Fig.  g.  In 
this  it  will  be  seen 
that  the  plain  faces 
of  the  stiles  and 
circular  rail  form 
junctions,  the  mould- 
ings all  being  mi- 
tcred.  The  miters 
are   curved   in  order 


Fi^.U, 


JOINER'S   WORK  ,J3 

to  have  all  the  members  of  the  mouldings  merge  in 
one  another  without  overwood.     Another  example  is 
shown   at   Fig.    lo,   where   the  circle    and    mouldings 
make  a  series  of  panels.     These  examples  are  quite 
sufficient  to  enable  the 
workman  to  deal  effect- 
ively with  every   prob- 
lem of  this  kind. 
The   workman   some- 
•les    finds    it   a    littk 
I  .fticult  to  lay  out  a  hip 
rafter  for  a  veranda  that 
has  a  curved  roof.      A 
very  easy  method  of  finding  the  curve  of  the  hip  is 
shown  at  Fig.  1 1.     Let  AB  be  the  length  of  the  angle 
or  seat  of  hip,  and  CO  the  curve;  raise  perpendicular 

en    AB,   as    shown, 

t    same     as    those    on 

i    DO,    and    trace 

j    through    the    points 

_^   •    obtained,    and    t  h  e 

-I   '    thing  is  done. 

jj  Another  simple 
(£  way  of  finding  the 
j  hip  for  a  single  curve 
•  is  shown  at  Fig.  12; 
!  AB  represents  the 
curve  given  the  com- 
mon rafter. 


Run > 


Now  lay  off  cny  number  of  lines  parallel  with  the 
seat  from  the  rise,  to  and  beyond  the  curve  AB,  as 
shown,  and  for  each  i.nrh  in  length  of  these  lines 
(between  rise  and  curve),  add  A  of  an  inch  to  the 
same  line  to  the  left  of  the  curve,  and  check.     After 


,84  MODERN  CARPENTRY 

all  lines  have  thus  been  measured,  run  an  off-hand 
curve  through  the  checks,  and  the  curve  will  represent 
the  corresponding  hip  at  the  center  of  its  back. 

To  find  the  bevel 
"7     or  backing  of  the  hip 
to  coincide  with  the 
plane  of  the  common 
rafter,  measure  back 
on  the  parallel  lines 
to   the   right  of  the 
curve    one-half     the 
thickness  of  the  hip 
and    draw    another 
curve,  which  will  be 
the  lines  on  the  side 
to  trim  to  from  the 
center  of  the  back. 
A  like  amount  must 
be     added     to    the 
plumb  cut  to  fit  the 
corner  of  deck.     Pro- 
ceed in  like  manner 
for  the  octagon  hip, 
but  instead  of  adding 


A,  add 


,1^  of  an  inch 


as  before  described. 

[While  this  is 
worked  out  on  a  giv- 
en rise  and  run  for  the 

rafter,  the  rule  is  applicable  to  any  rise  or  run,  as  the 
workman  will  readily  understand.] 

A  more  elaborate  system  for  obtaining  the  curve  of  a 
hip  rafter,  where  the  common  rafters  have  an  ogee  or 
concave  and  convex  shape,  is  shown  at  Fig.  I2J^.     This 


■^.'^■'-^■^isfc 


^vn 


C!i!}> 


j.>.T ". 


^«?^.-:^^:^^ripf. 


JOINER'S  WORK 


I  as 


i 


is  a  very  old  method,  and  is  shown — with  slight  varia- 
tions—in nearly  all  the  old  works  on  carpentry  and 
winery.  Draw  the  seat  of  the  common  rafter,  AB, 
and  r'.<v.  AC.  Then  draw  the  curve  of  the  common 
rafter,  C  .  Now  divide  the  base  line,  AB,  into  any 
number  .f  equal  spaces,  as  i,  2,  3,  4,  5,  etc.,  and  draw 
peijjci-  'icular  lines  to  construct  the  curve  CB,  as  I  O, 
2  0,  30,  40,  etc.  Now  draw  the  seat  of  the  valley,  or 
hip  rafter,  as  1  ^,  and  continue  the 
perpendicular  lines  referred  to  until 
they  meet  BD,  thus  establishing  the 
points  10,  II,  12,  13,  14,  etc.  From 
these  points  draw  lines  at  right 
angles  to  BD,  making  10  x  equal  in 
length  to  I  O,  and  1 1  x  equal  to  2  o; 


also  12  X  equal  to  3  o,  and  so  on.  When  this  has  been 
done  draw  through  the  points  indicated  by  x  the 
curve,  which  is  the  profile  of  the  valley  rafters. 

Another  method,  based  on  the  same  principles  as 
Fig.  12^,  is  shown  at  Fig.  13.  Let  ABCFED  represent 
the  plan  of  the  roof.  FCG  represents  the  profile  of  the 
wide  side  of  common  rafter.  First  divide  this  common 
rafter,  GC,  into  any  number  of  parts — in  this  case  6. 


m 


^^d.< 


ta« 


MODERN  CARPENTRY 


Transfer  these  points  to  the  miter  line  EB,  or,  what  ?i 
the  same,  the  line  in  the  plan  representing  the  hip 
rafter  From  the  points  thus  established  at  E,  erect 
perpendiculars  indefinitely  With  the  dividers  take 
the  distance  from  the  points  in  the  line  FE,  measur- 
ing to  the  points  in  the  profile  GC,  and  set  the  same 
off  on  corresponding  lines,  measuring  from  EB,  thus 
establishing  the  points   i,  2,  etc.;    then  a  line  traced 

through  these 
points  will  be  the 
required  hip  rafter. 
For  the  com- 
mon rafter,  on  th<; 
narrow  side,  con^ 
tinuethe  lines  from 
EB  parallel  with 
the  lines  of  the 
plan  DE  and  AB. 
Draw  AD  at  right 
angles  to  these 
lines.  With  the 
dividers,  as  before,  measuring  from  FE  to  the  points 
in  GC,  set  off  corresponding  distances  from  AD,  thus 
establishing  the  points  shown  between  A  and  H.  A 
line  traced  through  the  points  thus  obtained  will  be 
the  line  of  the  rafter  on  the  narrow  side. 

These  examples  are  quite  sufficient  to  enable  the 
workman  to  draw  the  exact  form  of  any  rafter  no  mat- 
ter what  the  curve  of  its  face  may  be,  or  whether  it  is 
for  a  veranda  hip,  or  an  angle  bracket,  for  a  cornice 
or  niche. 

Another  class  of  angular  curves  the  workman  will 
meet  with  occasionally,  is  that  when  raking  mould- 
ings are   used    to  work   in   level   mouldings,    as   for 


!^-f^& ^^^^ 


m 


JOINER'S  WORK 


127 


instance,  a  moulding  down  a  gable  that  is  to  miter. 
The  figures  shaded  in  Fig.  14  represent  the  mould- 
ing in  its  various  phases  and  angles.  Draw  th  out- 
line of  the  common  level  moulding,  as  shown  at  F,  in 
the  same  position  as  if  in  its  place  on  the  building. 
Draw  lines  through  as  many  prominent  points  in  the 
profile  as  may  be  convenient,  parallel  with  the  line  of 
rake.  From  the  same  points  in  the  moulding  draw  ver- 
tical lines,  as  shown  by  ill,  2,  3,  4  and  5,  etc.  From 
the  point  I,  square  with  the  lines  of  the  rake,  draw  iM, 


as  shown,  and  from  i  as  center,  with  the  dividers 
transfer  the  divisions  2,  3,  4,  etc.,  as  shown,  and  from 
the  points  thus  obtained,  on  the  upper  line  of  the  rake 
draw  lines  parallel  to  iM.  Where  these  lines  intersect 
with  the  lines  of  the  rake  will  be  points  through  which 
the  outline  C  may  be  traced. 

In  case  there  is  a  moulded  head  to  put  upon  a  raking 


-1 


i;8 


MODERN   CARPENTRY 


I 


'-^'>^ 


m 


gable,  the  moulding  D  shown  at  the  right  hand  must 
be  worker,  out  for  the  upper  side,  'ihe  manner  in 
which  this  is  done  is  self-evident  upon  examination 
of  the  drav'ng,  and  therc^fore  needs  no  special 
description. 

A  good  example  of  a  raking  moulding  and  its  appli- 
cations to  actual  work  is  shown  in  Fig.  15,  on  a  differ- 
ent scale.  The  ogee  moulding  at  the  lower  end  is  the 
regular  moulding,  while  the  middle  line,  ax,  shows 
the  shape  of  the  raking  moulding,  and  the  curve  on 


the  top  end,  cdo,  shows  the  face  of  a  moulding  that 
would  be  required  to  return  horizontally  at  that  point. 
The  manner  of  pricking  off  these  curves  is  shown  by 
the  letters  and  figures. 

At  Fig.  16  a  finished  piece  of  work  is  shown,  where 
this  manner  of  work  w'l!  be  required,  on  the  returns. 

Fig.  17  shows  the  same  moulding  applied  to  a 
curved  window  or  door  head.  The  manner  of  pricking 
the  curve  is  given  in  Fig.  18. 

At  No.  2  draw  any  line,  AD,  to  the  center  of  the 


1 


7    v:-  •f^.i 


JOINER'S   WORK 


129 


pediment,  meeting  the  upper  edge  of  the  upper  fillet 
ia  D,  and  intersecting  the  lines  AAA,  aa :,  bbb,  ccc, 


BBB  in  A,  o,  b,  c,  B,  E.    From  these  points  draw  lines 
aa,  bb,  cc,  BB,  EE,  tangents  to  their  respective  arcs; 


130 


MODERN  CARPENTRY 


^ 


^ig.  19. 


7 


1 


A 


V 


on  the  tangent  line  DE,  from  D,  make  Y)d,  D^,  D/ 
DE,  respectively  equal  to  the  listances  D</,  D^,  D/ 
DE  on  the  level  line  DE,  at  No.  i.  Through  the 
points  d,  e,  f,  E,  draw  da,  eb,  fc,  EB,  then  the  curve 
drawn  through  the  points  A,  a,  b,  c,  B,  will  be  the  sec- 
tion of  the  circular  moulding. 

Sometimes  mouldings  for  this  kind  of  work  are  made 

of  thin  stuff, 
-r^-  >  ^      and  are  bev- 

eled on  the 
back  at  the 
bottom  in 
such  a  man- 
ner that  the 
top  portion 
of  the  mem- 
ber hangs 
over,  which 
gives  it  the 
appearance 
of  being 
solid. 

^     ■  of  tills  kmd 

are  called 
"spring  mouldings,"  and  much  care  is  required  in 
mitering  them.  This  should  always  be  done  in  a 
miter  box,  which  must  be  made  for  the  purpose;  often 
two  boxes  are  required,  as  shown  in  Figs.  19-22.  The 
cuts  across  the  box  are  regular  miters,  while  the  angles 
down  the  side  are  the  same  as  the  down  cut  of  the 
rafter,  or  plumb  cut  of  the  moulding.  When  the  box 
is  ready,  place  the  mouldings  in  it  upside  down,  keep- 
ing the  moulded  side  to  the  front,  as  seen  in  Fig.  20, 


\A 


m 


T 


JOINER'S   WORK 


131 


making  sure  that  the  level  of  the  moulding  at  c   fits 
close  to  the  side  of  the  box. 

To  miter  the  rake  mouldings  together  at  the  top, 
the  box  shown  in  Fig.  21  is  used.  The  angles  on  the 
top  of  the  box  are 
the  same  as  the 
down  bevel  at  the 
top  of  the  rafter,  the 
sides  being  sawed 
down  square.  Put 
the  moulding  in  the 
box,  as  shown  in 
Fig.  22,  keeping  the 
bevel  at  c  flat  on  the 
bottom  of  the  box, 
and  having  the 
moulded  side  to  the 
front,  and  the  miter 
for  the  top  is  cut, 
which  completes  the 
moulding  for  one 
side  of  the  gable. 
The  miter  for  the 
top  of  the  moulding 
for  the  other  side  of 
the  gable  may  then 
be  cut. 

When  the  rake 
moulding  is  made  of 
the  proper  form  these 
boxes  are  very  con- 
venient; but  a  great 
deal  of  the  machine- 
made  mouldings  are        I'' 


L'l 


r 


ill 


,3a  MODERN   CARPENTRY 

not  of  the  proper  form  to  fit.  In  such  cases  the 
moulding  should  be  made  to  suit,  o  they  come  bad; 
although  many  use  the  mouldings  as  they  come  from 
the  factory,  and  trim  the  miters  so  as  to  make  them 

do. 

The    instructions  given,  however,  m  hif,'s.  13,  14,  15 

and  18  will  enable 
the     workman    to 
make  patterns  for 
what   he   retjuires. 
While     the 
"anslL'  bar"  is  not 
J    much   in  vogue  at 
"    the    present   time, 
the     methods     by 
which     it     is     ob- 
tained, maybe  ap- 
plied to  many  pur- 
poses, so  it  is  but 
proiHT  the  method 
should    be    em- 
bodied    in    this 
work.     In  Fig.  23, 
R    is    a    common 
sash  bar,  and  C  is 
the    angle    bar    of 
t  h  e    same    thick- 
ness.   Take  the  raking  projection,  11,  in  C,  and  set  the 
foot  of  your  compass  in   i  at  1?,  and  cross  the  middle 
of  the  bar  at  the  other  i ;  then  draw  the  pomts  2,  2,  3,  3, 
etc.,  parallel  to  li,  then   prick  your  bar  at  C  from  the 
ordinates  su  drawn  at  B,  which,  when  traced,  wdl  give 

the  angle  bar  ,•   j  * 

This  is  a  simple  operation,  and  may  be  applied  to 


Fig.2i, 


i^ 


JOINER'S  WORK 


»33 


-i 


many  other  cases,  and  for  enlarging  or  diminishing 

mouldings  or  other  work. 
The  next  fi'_[ure,   24,   gives  the   lines   for  a  raking 

moulding,  such  as  a  cornice  in  a  room  with  a  sloping 

ceiling.       As    may    be 

seen  from  the  diagram 

the     three    sections 

shown  are  drawn  equal 

in  thickness  to  miter  at 

the  angles  of  the  room. 
The  construction 

should  be  easily  under- 
stood.   When  a  straight 

moulding     is     mitered 

with  a  curved  one  the 

line  of   miter  is  some- 
times straight  and  sometimes  curved,  as  seen  at  Fig. 

18,  and  when  the  mouldings  are  all  curved  the  miters 

are  also  straight   and  curved,   as  shown    in   previous 

examples. 

If  it  is  desired  to  make  a  cluster  column  of  wood,  it 

is  first  necessary  to  make  a  standard  or  core,  which  must 

have  as  many  sides  as  there  are  to  be  faces  of  columns. 

Fig.  25  shows  how  the  work  is 
done.  This  shows  a  cluster  of 
four  columns,  which  are  nailed  to 
a  square  standard  or  core.  Fig. 
26  shows  the  base  of  a  clustered 
column.  These  are  blocks  turned 
in  the  lathe,  requiring  four  of 
them  for  each  base,  which  are  cut 
and  mitered  as  shown  in  Fig.  25. 
The  cap,  or  capital,  is,  of  course, 
cut  in  the  same  manner. 


Fig.  ^6. 


S.._=.-".c. 


»34 


MODERN  CARPENTRY 


i 


I* 


■')■ 


Laying  out  lines  for  hopper  cuts  is  often  puzzling, 
and  on  this  account  1  will  devote  more  space  to  this 
subject  than  to  those  requiring  less  explanations. 

Fig.  27  shows  an  isometric  view  of  three  sides  of  a 
hopper.  The  fourth  side,  or  end,  is  purposely  left 
out,  in  order  to  show  the  exact  build  of  the  hopper. 
It  will  be  noticed  that  AC  and  EC)  show  the  end  of  the 

work  as  squared 
up  from  the  bot- 
tom, and  that  HC 
shows  the  gain  of 
the  splay  or  flare. 
This  gives  the  idea 
of  what  a  hopper 
is,  though  the 
width  of  side  and 
amount  of  flare 
may  be  any  meas- 
urement that  may 
be  decided  upon. 
The  difficuUy  in 
this  work  is  to  get 
the  proper  lines  for  the  miter  and  for  a  butt  cut. 

Let  us  suppose  the  flare  of  the  sides  and  ends  to  be 
as  shown  at  Fig.  28,  though  any  flare  or  inclination 
will  answer  equally  well.  This  diagram  and  the  plan 
exhibit  the  method  to  be  employed,  where  the  sides 
and  ends  are  to  be  mitered  together.  To  obtain  the 
bevel  to  apply  for  the  side  cut,  use  A'  as  center,  B'  as 
radius,  and  CDF  para. lei  to  BF.  Project  from  B  to 
D  oarallel  to  XY.  Join  AD,  which  gives  the  bevel 
required,  as  shown.  If  the  top  edge  of  the  stuff  is  to  be 
horizontal,  as  shown  at  B'G',  the  bevel  to  apply  to  the 
edge  will  be  simply  as  shown  in  plan  by  BG;   but  if 


. (     -;:' 


.5«?*«  :i5MRL. 


JOINER'S      .'ORK 


'35 


the  edge  of  the  stuff  is  to  be  square  to  the  side,  as 
shown  at  WC,  Fig.  29,  the  bevel  must  be  obtained  as 
follows:  Produce  EB'  to  D',  as  indicated.  Fig.  29. 
With  B  as  center,  describe  the  arc  from  C,  which 
gives  the  point  D.     Project  down  from  D,  makin^j  DF 


parallel  to  CC,  as  shown.  Project  from  C  parallel  to 
XY.  This  will  give  the  point  D.  Join  BD,  and  this 
will  give  the  bevel  line  required.  At  A,  Tig.  31,  is 
shown  the  application  of  the  bevel  to  the  side  of  the 
stuff,  and  at  B  the  application  of  the  bevel  to  the  edge 
of  the  stuff.  When  the  ends  butt  to  the  sides,  as  indi- 
cated at  H,  Fig.  30,  the  bevel,  it  will  he  noticed,  is 
obtained  in  a  similar  manner  to  that  shown  at  Fig  28. 
It  is  not  often  that  simply  a  butt  joint  is  used  between 


IITT^' 


•.n 


136 


MODERN   CARPENTRY 


I 


U 
if 


the  ends  and  sides,  but  the  ends  are  usually  housed 
into  the  sides,  as  indicated  by  the  dotted  lines  shown 
at  H,  Fig.  30. 

Another  system,  which  was  first  taught  by  the  cele- 
brated   Peter    Nicholson,    and    afterwards    by   Robert 

Riddeil,  o^ 
P  h  i  1  a  d  e  1  • 
I)hia,  is  ex- 
plained in 
t  h  e  follow- 
i  n  g  :  T  h  t' 
illustra- 
tion shown  at 
I'^ig.  32  is  in- 
tended  to 
show  how  to 
find  the  lines 
for  cutting 
butt  joints 
for  a  hopper 
Construct  a 
right  angle, 
as  A,  B,  C, 
Fig.  32,  con- 
tinue A,  H 
pastK.  From 
K,  B  make 
the  inclination  of  the  sides  of  the  hopper,  2,  3. 

Draw  3,  4  at  right  angles  with  3,  2;  take  3  as  center, 
and  strike  an  arc  touching  the  lower  line,  cutting  in  4. 
Draw  from  4,  cutting  the  miter  line  in  5;  from  5  square 
draw  a  line  cutting  in  6.  join  it  and  B;  this  gives  bevel 
W,  as  the  direction  of  cut  on  the  surface  of  sides.  To 
find  the  butt  joint,  take  any  two  points,  A,  C,  on  the 


JOINICkS    WORK 


'37 


rijiht  anj,'it .  equally  distant   from   H,  make  the  anglr 

H.  K.  L.  ..qual  that  of  3.  K.  L.  shown  on  the  k-ft;  from 

H  tlraw  through  point  I.;    now  take  C  as  a  center,  and 

strike    an  arc,   tnuchinf,'    line  BL.      From  A  draw  a 

line  touching  thr  arc  at  II,  and  cuttinjj  the  extended 

line   throujih    H 

in  N,  thus  fixing,' 

N    as    a    point. 

Then   by  draw- 

i  n  g    from    C 

throuK'h    N,    \vc 

get     the     bevel 

X   for  the  butt 

joint.     Joints 

on  the  ends  of 

timbers  running 

horizontally    in 

tapered   framed 

structures,  when 

the    plan    is 

square    and  the 

inclinations 

equal,    may    be 

found     by    this 

method. 

The  backing 
of  a  hip  rafter  may  also  be  obtained  by  this  method,  as 
shown  at  J,  where  the  pitch  line  is  used  as  at  2,  3, 
which  would  be  the  inclination  of  the  roof. 

The  solution  just  rendered  is  intended  only  for  hop- 
pers having  right  angles  and  equal  pitches  or  splays, 
as  hoppers  having  acute  or  obtuse  angles,  must  be 
treated  in  a  slightly  different  way. 

Let  us  suppose  a  butt  joint  for  a  hopper  having  an 


138 


MODERN  CARPENTRY 


acute  angle,  such  as  shown  at  A,  B,  C,  Fig.  33,  and 
with  an  inclination  as  shown  at  2,  3.  Take  any  two 
points,  A,  C,  equally  distant  from  B.  Join  A,  C, 
bisect  this  line  in  P,  draw  through  P,  indefinitely. 
Find  a  bevel  for  the  side  cut  by  drawing  3,  4,  square 
with  2,  3;  take  3  as  a  center,  and  strike  an  arc,  touch- 
ing the  lower  line  cutting  in  4;  draw  from  4,  cutting 


I: 


•  1 


!l 


the  miter  line  in  5,  and  from  it  square  draw  a  line 
cutting  in  6.  Join  6,  B,  this  gives  bevel  W,  for  direc- 
tion of  cut  on  the  surface  of  inclined  sides. 

The  bevel  for  a  butt  joint  is  found  by  drawing  C,  8, 
square  with  A,  B;  make  the  angle  8,  K,  L,  equal  that 
of  3,  K,  L,  shown  on  the  left.  Draw  from  8  through  point 
L;  take  C  as  a  center  and  strike  an  arc  touching  the 
line  8,  L;   draw  from  A,  touching  the  arc  at  D,  cutting 


JOINER'S  WORK 


139 


the  line  from  P,  in  D,  making  it  a  point,  then  by 
drawing  from  C,  thro  ^^h  D,  we  get  the  bevel  X  for 
the  butt  joint. 

As  stated  regarding  the  previous  illustration,  the 
backing  for  a  hip  in  a  roof  having  the  pitch  as  shown 
at  2,  3,  may  be  found  at  the  bevel  J.     The  same  rule 


also  applies  to  end  joints  on  timbers  placed  in  a  hori- 
zontal double  inclined  frame,  having  an  acute  angle 
same  as  described. 

Having  described  the  methods  for  finding  the  butt 
joints  in  right-angled  and  acute-angled  hoppers,  it  will 
be  proper  now  to  define  a  method  for  describing  an 
obtuse-angled  hopper  having  butt  joints. 

Let  the  inclination  of  the  sides  of  the  hopper  be 


"i 

U 

t 

• 

(' 

] 

\' 

'    '* 

li 

li 

J 

1                       '.        : 

'      i!  : 

.    i 

1  : 

I;    i 


(IP 
I' 


140 


MODERN  CARPENTRY 


exhibited  at  the  line  2,  3,  and  the  angle  of  the  obtuse 
corner  of  the  hopper  at  A,  B,  C,  then  to  find  the  joint, 
take  any  two  points,  A,  C,  equally  distant  from  B, 
join  these  points,  and  divide  the  line  at  P.  Draw 
through  P  and  B,  indefinitely.  At  any  distance  below 
the  side  A,  B,  draw  the  line  2,  6;  make  3,  4,  square 
with  the  inclination.  From  3,  as  a  center,  describe 
an  arc,  touching  the  lower  line  and  cutting  in  4;  from 
4  draw  to  cut  the  miter  line  in  5,  and  from  it  square 


down  a  line  cutting  in  6,  join  6,  B,   and  we  get  the 
bevel  W   for  cut  on  surface  sides. 

The  bevel  for  the  butt  joint  is  found  by  drawing  C, 
D,  square  with  B,  A,  and  making  the  angle  D,  K,  L 
equal  to  that  of  3,  K,  L  on  the  left.  From  C,  as  a 
center,  strike  an  arc,  touching  the  line  D,  L;  then 
from  A  draw  a  line  touching  the  arc  H.  This  line 
having  cut  through  P,  in  N,  fixes  N  as  a  point,  so  that 
by  drawing  C  through  N  an  angle  is  determined,  in 
which  is  bevel  X  for  the  butt  joint. 


JOINER'S   WORK 


141 


To  obtain  the  bevels  or  miters  is  a  simple  matter  to 
one  who  has  mastered  the  foregoing,  as  evidenced  by 
the  following: 

Fig.  34  shows  a  right-angled  hopper;  its  sides  may 
stand    on    any  inclination,   as  AB.      The  miter  line. 


2,  W,  on  the  p.un.  being  fixed,  draw  B,  C  square  with 
the  inclination.  Then  from  B,  as  center,  strike  an  arc, 
touching  the  base  line  and  cutting  in  CD.  From  CD 
draw  parallel  with  the  base  line,  cutting  the  miters  in 
F  and  E;  and  from  these  points  square  down  the  lines, 
cutting  in  3  and  4.    From  2  draw  through  3;  this  gives 


oevel  W  for  the  direction  of  cut  on  the  surface  sides. 
Now  join  2,  4,  this  gives  bevel  X  to  niiter  the  edges, 
which  in  all  cases  must  be  square,  in  order  that  bevels 
may  be  properly  applied. 
Fig.  35  shows  a  plan  forming  an  acute-angled  hop- 


kI 


i!f 


14s 


MODERN  CARPENTRY 


per,  the  miter  line  being  2,  W.  The  sides  of  this  plan 
are  to  stand  on  the  inclination  AH.  Draw  BC  square 
with  the  inclination,  and  from  B,  as  center,  strike  an 
arc,  touching  the  base  line  and  cutting  in  CD.  Draw 
from  CD,  cutting  the  miter  line  at  E  and  F;  from  these 
points  square  down  the  lines,  cutting  in  3  and  4.  From 
2  draw  through  4,  which  will  give  bevel  W  to  miter 
the  edges  of  sides.  Now  join  2,  3,  which  gives  bevel 
X  for  the  direction  of  cut  on  the  surface  of  sides. 

Fig.  36  shows  an  obt'ise  anj,dcd  hopper,  its  miter  line 
on  the  plan  being  2  W,  and  the  inclination  of  sides 


I 


AB.  Draw  BC  square  with  the  inclination,  and  from 
B  as  center  strike  an  arc,  touching  the  base  line  and 
cutting  CD.  Draw  from  CD,  cutting  the  miter  in  F 
and  E.  From  these  points  square  down  the  lines,  cut- 
ting the  base;  then  by  drawing  from  2  through  the 
point  below  E,  we  get  bevel  W  for  the  direction  of 
ci.<^-  on  the  surface  of  sides,  and  in  like  manner  the 
point  below  F  being  joined  with  2,  gives  bevel  X  to 
miter  the  edges. 

It  will  be  noticed  that  the  cuts  for  the  three  differ- 
ent angles  are  obtained  on  exactly  the  same  principle, 
without  the  slightest  variation,  and  so  perfectly  sim- 
ple as  to  be  understood  by  a  glance  at  the  drawing. 
The  workman  will  notice  that  in  each  of  the  angles  a 


JOINER'S  WORK 


M3 


»44 


MODERN   CARPENTRY 


line  from  C,  cutting  the  miter,  invariably  gives  a  direc- 
tion for  the  surface  of  sides,  and  the  line  from  D 
directs  the  miter  on  their  edges. 

Unlike  many  other  systems  employed,  this  one  meets 
all  and  every  condition,  and  is  the  system  that  has 
been  employed  by  high  class  workmen  and  millwrights 
for  ages. 

One  more  example  on  hopper  work  and  I  am  done 

with  the  subject:      Suppose  it  is  desired  to  build  a 

hopper  similar  to  the  one  shown  at  Fig.  37,  several 

new  conditions 
\ 

%.  38. 


will  be  met  with, 
as  will  be  seen  by 
an  examination  of 
the  obtuse  and 
acute  angles,  L 
and  P.  In  order  to 
work  this  out 
right  make  a 
diagram  like 
that  shown  at  Fig.  38,  where  the  line  AD  is  the  given 
base  line  on  which  the  slanting  side  of  hopper  or  box 
rises  at  any  angle  to  the  base  line,  as  CB,  and  the 
total  height  of  the  work  is  represented  by  the  line 
B,  E.  By  this  diagram  it  will  be  seen  that  the  hori- 
zontal lines  or  bevels  of  the  slanting  sides  are  indi- 
cated by  the  bevel  Z. 

Having  got  this  diagram,  which  of  course  is  not 
drawn  to  scale,  well  in  hand,  the  ground  plan  of  the 
hopper  may  be  laid  down  in  such  a  shape  as  desired, 
with  the  sides,  of  course,  having  the  slant  as  given  in 

Fig.  38. 

Take  T2,  3S,  Fig.  37,  as  a  part  of  the  plan,  then  set 
off  the  width  of  sides  equal  to  C,  B,  as  shown  in  Fig.  38. 


JOINER'S  WORK 


145 


These  are  shown  to  intersect  at  P,  L  above;  then  draw 
lines  from  P,  L  through  2,  3,  until  they  intersect  at  C, 
as  the  dotted  lines  show.  Take  C  as  a  center,  and 
with  the  radius  A,  describe  the  semi-circle  A,  A,  and 
with  the  same  radius  transferred  to  C,  Fig.  38,  describe 
the  arc  A,  13,  as  shown.  Again,  with  the  same  radius, 
set  off  A,  B,  A,  B  on  Fig.  37,  cutting  the  semi-circle  at 
B,  as  shown.  Now  draw  through  B,  on  the  right, 
parallel  with  S,  3,  cutting  at  J  and  F;  square  over  F, 
H  and  J,  K,  and  join  H,  C;  this  gives  bevel  X,  as  the 
cut  for  face  of  sides,  which  come  together  at  the  angle 
shown  at  3.  The  miters  on  the  edge  of  stuff  are 
parallel  with  the  dotted  line,  L,  3.  This  is  the  acute 
corner  of  the  hopper,  and  as  the  edges  are  worked  off 
to  the  bevel  2,  as  shown  in  Fig.  38,  the  miter  must  be 
correct. 

Having  mastered  the  details  of  the  acute  corner,  the 
square  corner  at  S  will  be  next  in  order  The  first  step 
is  to  join  K,  V,  which  gives  the  bevel  V,  for  the  cut 
on  the  face  of  sides  on  the  ends,  which  form  the  square 
corners.  The  method  of  obtaining  these  lines  is  the 
same  as  that  explained  for  obtaining  them  for  the 
acute-angled  corner,  as  shown  by  the  dotted  lines, 
Fig-  35.  As  the  angles,  S,  T,  are  both  square,  being 
right  and  left,  the  same  operation  answers  both,  that 
\s,  the  bevel  Y  does  for  both  corners. 

Coming  to  the  obtuse  angle,  P,  2,  we  draw  a  line 
B,  E,  on  the  left,  parallel  with  A,  2,  cutting  at  E,  as 
shown  by  dotted  line.  Square  over  at  E,  cutting 
T,  A,  2  at  N;  join  N,  C,  which  will  give  the  bevel  \V, 
which  is  the  angle  of  cut  for  face  of  sides.  The  miters 
on  edges  are  found  by  drawing  a  line  parallel  with  P,  2. 

In  this  problem,  like  Fig.  34,  every  line  necessary 
to  the  cutting  of  a  iiopper  after  the  plan  as  shown  by 


146 


MODERN  CARPENTRY 


mi 


the  boundary  lines  2,  3,  T,  S.  is  complete  and  exhaust- 
ive, but  it  must  be  understood  that  in  actual  work  the 
spreading  out  of  the  sides,  as  here  exhibited,  will  not 
be  necessary,  as  the  angles  will  find  themselves  when 
the  work  is  put  together.     When  the  plan  of  the  base — 
which  is  the  small  end  of  the  hopper  in  this  case— is 
given,  and  the  slant  or  inclination  of  the  sides  known, 
the  rest  may  be  easily  obtained.     In  order  to  become 
thoroughly  conversant   with    the    problem,    I    would 
advise  the  workman  to  have  the   drawing  made   on 
cardboard,  so  as   to   cut   out   all   the  outer  lines,  in- 
cluding   the   open   corners,    which   form    the   miter?, 
leaving  the   whole  piece  loose.      Then   make   slight 
cuts  in  the  back  of  the  cardboard,  opposite  the  lints 
2,  3,  S,  T,  just  deep  enough  to  admit  of  the  cardboard 
being  bent  upwards  on  the  cut  lines  without  breaking. 
Then  run  the  k  life  along  the  lines,  which  indicates  the 
edges  of  the  hopper  sides.     This  cut  must  be  made  on 
the  face  side  of  the  drawing,  so  as  to  admit  of  the 
edge     ■    -ig  turned  downwards.      After  all   cuts  are 
made  raise  the  sides  until  the  corners  come  closely 
together,   and   let  the  edges   fall   level,   or  in  such  a 
position  that  the  miters  come  closely  together.     If  the 
lines  have  been  drawn  accurately  and  the  cuts  made 
on  the  lines  in  a  proper  manner,  the  work  will  adjust 
itself  nicely,  and  the  sides  will  have  the  exact  inclina- 
tion shown  at   Fig.   38,   and  a  perfect  model  of  the 
work  will  be  the  result. 

This  is  a  very  interesting  problem,  and  the  working 
out  of  it,  as  suggested,  cannot  but  afford  both  profit 
and  pleasure  to  the  young  workman. 

From  what  has  preceded,  it  must  be  evident  to  the 
workman  that  the  lines  giving  proper  angles  and 
bevels  for  the  corner  post  of  a  hopper  must  of  neces- 


rr 


JOINER'S   WORK 


»47 


sity  give  the  proper  lines  for  the  corner  post  for  a  pyr- 
a..iidai  building,  such  as  a  railway  tank  frame,  or  any 
similar  structure.  True,  the  position  of  the  post  is 
inverted,  as  in  the  hopper,  its  top  falls  outward,  while 
in  the  timber  structure  the  top  inclines  inward;  but  this 
makes  no  difference  in  the  theory,  all  the  operator  has 
to  bear  in  mind  is  that  the  hopper  in  this  case  is  reversed 
—inverted.  Once  the  proper  shape  of  the  corner  post 
has  been  obtained,  all  other  bevels  can  readily  be 
found,  as  the  side  cuts  for  joists  and  braces  can  be 
taken  from  them.  A  study  of  these  two  figures  in  this 
direction  will  lead  the  student  up  to  a  correct  know! 
edge  of  tapered  framing. 


p\ 


CHAPTER    II 


COVERING    SOLIDS,    CIRCULAR     WORK,     DOVETAILING    AND 

STAIRS 

There  are  several  ways  to  cover  a  circular  tower  roof. 
Some  arc  covered  by  bending  the   boarding  around 


them,  while  others  have  the  joints  of  the  coverii  g  ver- 
tical, or  inclined.  In  either  case,  the  boarding  has  to 
be  cut  to  shape.     In  the  first  instance,  where  tht  joints 

148 


JOINER'S   WORK 


149 


are  horizontal,  the  covering  must  be  curved  on  both 
edges. 

At  Fig.  39  I  show  a  part  plan,  elevation,  and  develop- 
ment of  a  conical  tower  roof.     ABC  shows  half  the 
plan;    DO  and  EO  show  the  inclination  and  height  of 
the  tower,  while  EH  and  EI  show  the 
development  of  the   lower  course  of 
covering.     This  is  obtained  by  using 
O  as  a  center,  with  OE  as  radius,  and 
striking  the  curve   EI,   which   is   the 
lower  edge  of  the  board,   and  corre- 
sponds to  DE  in  the  elevation.     From 
the  same  center  O,  with  radius  OF, 
describe  the  curve  FH,  which   is  the 
joint  GF  on  the  elevation.    The  board, 
EFHI,  may  be  any  convenient  width, 
as  may  also  the  other  boards  used  for 
covering,  but  whatever  the  width  de- 
cided upon,  that  same  width  must  be 
continued     throughout    that    course. 
The  remaining  tiers  of  covering  must 
be  obtained  in  the  same  way.      The 
joints  are  radial  lines  from  the  center 
O.      Any  convenient  length   of  stuff 
over  the  distance  of  three  ribs,  or  raft- 
ers, will  answer.     This  solution  is  ap- 
plicable to  many  kinds  of  work.     The 
rafters  in  this  case  are  simply  straight  scantlings;  the 
bevels  for  feet  and  points  may  be  obtained  from  the 
diagram.      The   shape   of    a    "gore,"    when    such    is 
required,  is  shown  at  Fig.  40,  IJK  showing  the  base, 
and  L  the  top  or  apex.     The  method  of  getting  it  out 
will  be  easily  understood  by  examining  the  diagram. 
When  "gores"  are  used  for  covering  it  will  be  necessary 


Fig.  40. 


JBb 


150 


MODERN   CARPENTRY 


♦',) 


1 


to  have  cross-ribs  n.uied  in  between  the  rnfters,  ana 
these  must  be  cut  to  the  sweep  uf  the  cir  ic,  where 
they  are  nailed  in,  so  that  i  rib  place<l  in  'aalf  way  up 
will  require  only  to  be  luilf  the  diameter  of  the  base, 
and  the  other  ribs  must  be  cut  accor-lingly. 

To  cover  a  domici.  roof  with  horizontal  boarding  we 
pro^^cd  in  the  .wanner  shown  in  Fig.  41,  where  AHC 


E 

• 

71 

M) 

^^^^^^ 

^"^^Ss^^A  Jt/ 

T^ 

'^vn 

J 

\W 

f 

^ 

Flij.  11. 


is  a  vertical  section  hrough  the  axis  of  a  circular 
dome,  and  it  is  requ  red  t<>  cover  this  dome  hori- 
zontally. Bisect  th(  base  i  i  the  point  D.  and  draw 
DBE  perpendicular  to  AC,  cutting  thi  circumference 
in  B.  Now  divide  the  arc,  BC,  into  equal  parts, 
that  each  part  will  be  rather  less  than  th<'  width  of 
a  board  and  io!n  th--'  no'.nts  r>f  division  Hv  ^itr^icfht 
lines,  which  will  form  a.  inscribed  polygon  of  so  many 
sides;  and  through  thesv  points  draw  lines  parallel  to 


JOINER'S  WORK 


«5» 


the  l)ase  AC,  m«'etinf(  the  opposite  sides  of  the  circum- 
ference. The  trapezoids  formed  by  the  sides  of  the 
polygon  and  the  horizontal  lines  may  then  be  regarded 
as  the  sections  of  so  many  frustrums  of  cones;  whence 
results  thf  foHuwinj^  mofie  of  procedure:  Produce, 
until  tht.y  mtn  t  the  line  DE,  the  lines  FG,  etc.,  form- 
infi  the  sides  of  the  polygon.  Then  to  describe  a 
lioard  whicii  corresponds  to  the  surface  of  one  of  the 
zones,  as  FG,  of  which  the  trapezoid  is  a  section  from 


F>g.^^'^ 


the  1  oir    }.,  whe       the  line  FG  prodi    eu  meets  DE, 
with  radi'    EF,  EG  describe  two  arcs  and  cut  off 

the  t  the  boaid  K  on  the  line  of  a  radius  EK. 

'i  '^e      her  boards  are  described  in  the  same  manner. 

T'-^cre  r-'  many  other  solids,  some  oT  which  it  is 
p  ssible  the  workman  may  be  called  uj  n  to  cover, 
but  15  space  will  not  admit  o.f  us  H.iscussinji  them  a!!, 
H'  will  illustrate  one  example,  which  includes  within 
itself  the  (uinciples  by     !iich  almost  .uiy  other  so'' 


»5> 


MODERN  CARPENTRY 


P^! 


may  be  dealt  with.     Let  us  suppose  a  tower,  having  a 
domical  roof,  rising  from  another  roof  having  an  incll 
nation  as  shown  at  BC,  Fig.  42,  and  we  wish  to  board 

it  with  the  joints  of 
the  boards  on  the 
same  inclination  as 
that  of  the  roof 
through  which  the 
tower  rises.  To 
accomplish  this,  let 
A,  B,  C,  D,  Fig.  42, 
be  the  seat  of  the 
generating  section; 
from  A  draw  AG 
perpendicular  to 
AB,  and  produce 
CD  to  meet  it  in  E; 
on  A,  E  describe  the 
semi -circle,  and 
transfer  its  perim- 
eter to  E,  G  by 
dividing  it  into 
equal  parts,  and 
setting  off  corre- 
sponding divisions 
on  E,  G.  Through 
the  divisions  of  the 
semi -circle  draw 
lines  at  right  angles 
to  AE,  producing 
them  to  meet  the 
lines  A,  D  and  B,  C  in  i,  k,  I,  m,  etc.  Through  the 
divisions  on  E,  G,  draw  lines  perpendicular  to  them; 
then  through  the  intersections  of  the  ordinates  of  the 


JOINER'S  WORK 


153 


semi-circle,  with  the  line  AD  draw  the  lines  «,  a,  k,  z, 
/,  jr,  etc.,  parallel  to  AG,  and  where  these  intersect  the 
perpendiculars  from  EG,  in  points  a,  e,  _y,  ;r,  w,  v, 
«,  etc.,  trace  a  curved  line,  GD,  and  draw  parallel 
to  it  the  curved  line  HC;  then  will  DC,  HG  be  the 
development  of  the  covering  required. 

Almost  any  description  of  dome,  cone,  ogee  or 
other  solid  may  be  developed,  or  so  dealt  with  under 
the  principle  as 
shown  in  the 
foregoing,  that 
the  workman,  it 
is  hoped,  will  ex- 
perience  but 
little  difficulty  in 
laying  out  lines 
for  cutting  mate- 
rial to  cover  any 
form  of  curved 
roof  he  may  be 
confronted  with. 

Another  class 
of  covering  is 
that    of    making 

soffits  for  splayed  doors  or  windows  having  circular  or 
segmental  heads,  such  as  shown  in  Fig,  43,  which  exhib- 
its a  door  with  a  circular  head  and  splayed  jambs. 
The  head  or  soffit  is  also  splayed  and  is  paneled  as 
shown.  In  order  to  obtain  the  curved  soffit,  to  show 
the  same  splay  or  angle,  from  the  vertical  lines  of  the 
door,  proceed  as  follows:  Layout  the  width  of  the 
doorway,  showing  the  splay  of  the  jambs,  as  at  C,  B  and 
L,  P;  extend  the  angle  lines,  as  shown  by  the  dotted 
lines,  to  A,  which  gives  A,   B  as  the  radius  of  the 


w 

1^ 

/ 

Jfc                  "V 

1     \FigA4,. 

/J 

IJ 


154 


MODERN  CARPENTRY 


inside  curve,  and  A,  C  as  radius  of  the  outside  curve. 
These  radii  correspond  to  the  radii  A,  B  and  A,  C  in 
Fig-  43;  the  figure  showing  the  flat  plan  of  the  pan- 
eled soffit  complete.  To  find  the  development,  Fig. 
43,  get  the  stretch-out  of  the  quarter  circle  2  and  3, 
shown  in  the  elevation  at  the  top  of  the  doorway,  and 


«--< 


make  2,  3  and  3B,  Fig.  43.  equal  to  it,  and  the  rest  of 
the  work  is  very  simple. 

If  the  soffit  is  to  be  laid  off  into  panels,  as  shown  at 
Fig.  44,  it  is  best  to  prepare  a  veneer,  having  its  edges 
curved  similar  to  those  of  Fig.  43,  making  the  veneer 
of  some  flexible  wood,  such  as  basswood,  elm  or  the 
like,  that  will  easily  bend  over  a  form,  such  as  is 
shown  at  Fig.  44,  The  shape  of  this  form  is  a  portion 
of  a  cone,  the  circle  L  being  less  in  diameter  than  the 


JOINER'S  WORK 


155 


circle  P.  The  whole  is  covered  with  staves,  which,  of 
course,  will  be  tapered  to  meet  the  situation.  The 
veneer,  x,  x,  etc.,  Fig.  43,  may  then  be  bent  over  the 
form  and  finished  to  suit  the  conditions.  If  the 
mouldings  used  in  the  panel  work  are  bolection  mould- 
ings, they  cannot  be  planted  in  place  until  after  the 
veneer  is  taken  off  the  form. 

This  method  of  dealing  with  splayed  work  is  appli- 
cable to  windows  as  well  as  doors,  to  circular  pews  in 


churches  and  many  other  places  where  splayed  work 
is  required. 

A  simple  method  of  finding  the  veneer  for  a  soffit  of 
the  form  shown  in  Fig.  43  is  shown  at  Fig.  45.  The 
splay  is  seen  at  C,  from  which  a  line  is  drawn  on  the 
angle  of  the  splay  to  B  through  which  the  vertical  line 
A  passes.     B  forms  the  center  from  which  the  veneer 


tt1  ■  J 


11 


m  -I 


li     1 


156 


MODERN  CARPENTRY 


is  descriDed.  A  is  the  center  of  the  circular  head,  for 
both  inside  and  outside  curves,  as  shown  at  D.  The 
radial  linos  centering  at  B  show  how  to  kerf  the  stuff 
when  necessary  for  bending.  The  line  E  is  at  right 
angles  with  the  line  CB,  and  the  veneer  CE  is  the 
proper  length  to  run  half  way  around  the  soffit.  The 
jtiints  are  radial  lines  just  as  shown. 

A  method  for  ob- 
taining the  correct 
shape  of  a  veneer 
for  a  gothic  splayed 
window  or  door- 
head,  is  shown  at 
Fig.  46;  E  shows 
the  sill,  and  line 
BA  the  angle  of 
splay.  BC  shows 
the  outside  of  the 
splay;  erect  the  in- 
side line  F  to  A, 
and  this  point  will 
form  the  center 
from  which  to  de- 
cribe  the  curve  or 
^'g-  *7.  veneer  G.      This 

veneer  will  be  the  proper  shape  to  bend  in  the  soffit 
on  either  side  of  the  window  head. 

The  art  of  dovetailing  is  almost  obsolete  among 
carpenters,  as  most  of  this  kind  of  work  is  now  done 
by  cabinet-makers,  or  by  a  few  special  workmen  iu 
the  factories.  It  will  be  well,  however,  to  preserve  the 
art,  and  every  young  workman  should  not  rest  until  he 
can  do  a  good  job  of  work  in  dovetailing;  he  wiii  not 
find  it  a  difficult  operation. 


JOINER'S    WORK 


157 


There  are  three  kinds  of  dovetailing,  i.e.,  the  com- 
mon dovetail,  Fijj.  47;  the  lapped  dovetail,  Fig.  48, 
and  the  secret,  or  mitered  dovetail,  Fig.  49.  These 
may  be  subdivided  into  other  kinds  of  dovetailing, 
but  there  will  be  but  little  difference. 

The  common  dovetail  is  the  strongest,  but  shows  the 
ends  of    the  dovetails   on  both  faces  of  the  angles, 


Fig.  48. 


and  's,  therefore,  only  used  in  -^  h  places  as  that 
of  a  drawer,  where  the  extei  A  angle  is  not 
seen. 

The  lapped  dovetail,  where  the  ends  of  the  dovetails 
show  on  one  side  of  the  angle  only,  is  used  in  such 
places  as  the  front  of  a  drawer,  the  side  being  only 
seen  when  opened. 

In  the  miter  or  secret  dovetail,  the  dovetails  are  not 
seen  at  all.     It  is  the  weakest  of  the  three  kinds. 


i.'U 


158 


MODERN  CARPENTRY 


At  Figs.  50  and  51  I  show  two  methods  of  dovetail- 
ing hoppers,  trays  and  other  splayed  work.  The 
reference  letters  A  and  B  show  that  when  the  work  is 
together  A  will  stand  directly  over  B.     Care  must  be 


11 


^ 


!■ 


Fig.  50. 


taken  when  preparing  the  ends  of  stuff  for  dovetailing 
for  hoppers,  trays,  etc.,  that  the  right  bevels  and 
angles  are  obtained,  according  to  the  rules  explained 


Fig.  51 


for  finding  the  cuts  and  bevels  for  hoppers  and  work 
of  a  similar  kind,  in  the  examples  given  previously. 
All  stuff  for  hopper  work  intending  to  be  dovetailed 


JOINER'S   WORK 


«S9 


must  be  prepared  with  butt  joints  before  the  dovetails 
are  laid  out.  Joints  of  this  kind  may  be  made  com- 
mon, lapped  or  mitered.  In  making  the  latter  much 
skill  and  labor  will  be  required. 

Stair  building  and  handrailing  combined  is  a  science 
in  itself,  and  one  that  taxes  the  best  skill  in  the  mar- 
ket, and  it  will  be  impossible  for  me  to  do  more  than 
touch  the  subject,  and  that  in  such  a  manner  as  to 
enable  the  workman  to  lay  out  an  ordinary  straight 
flight  of  stairs.  For  further  instructions  in  stair 
building  I  would  refer  my  readers  to  some  one  or 
two  of  the  many  works  on  the  subject  that  can  be 
obtained  from  any  dealer  in  mechanical  or  scientific 
books. 

The  first  thing  the  stair  builder  has  to  ascertain  is  the 
dimension  of  the  space  the  stairs  are  to  occupy;  then 
he  must  get  the  height,  or  the  risers,  and  the  width  of 
the  treads,  and,  as  architects  generally  draw  the  plan 
of  the  stairs,  showing  the  space  they  are  to  occupy 
and  the  number  of  treads,  the  stair  builder  has  only  to 
measure  the  height  from  floor  to  floor  and  divide  by 
the  number  of  risers  and  the  distance  from  first  to  last 
riser,  and  divide  by  the  number  of  treads.  (This 
refers  only  to  straight  stairs.)  Let  us  take  an  exam- 
ple: Say  that  we  have  ten  feet  of  height  and  fifteen 
feet  ten  inches  of  run,  and  we  have  nineteen  treads; 
thus  fifteen  feet  ten  inches  divided  by  nineteen  gives 
us  ten  inches  for  the  width  of  the  tread,  and  we  have 
ten  feet  rise  divided  by  twenty  (observe  here  that 
there  is  always  one  more  riser  than  tread),  which  gives 
us  six  inches  for  the  height  of  the  riser.  The  pitch- 
board  must  now  be  made,  and  as  all  the  work  has 
to  be  set  out  from  it,  care  must  be  taken  to  make  it 
exactly  right.     Take  a  piece  of  board,  same  as  shown 


i6o 


MODERN  CARPENTRY 


F  "^ 


in  Fig.  52,  about  half  an  inch  thick,  dress  it  and  square 
the  side  and  end,  A,  B,  C;  set  off  the  heij^ht  of  the 
rise  from  A  to  B,  and  the  width  of  the  trend  from  B 
toC;  now  cut  the  line  AC,  and  the  pitch-board  is  com- 
plete, as  shown  in  Fig.  53.  This  may  be  done  by  the 
steel  square  as  shown  at  Fig.  54.  To  get  the  width  of 
string-boards  draw  the  line  AB,  Fig.  53;  add  to  the  len},fth 
of  this  line  about  half  an  inch  more  at  A,  the  margin 
to  be  allowed,  and  the  total  will  be  the  width  of 
string-boards.     Thus,  say  that  we  allow  three  inches 


for  margin,  one-half  inch  to  be  left  on  the  under  side 
of  string-board,  will  make  the  width  of  string-boards 
in  this  case  about  nine  inches.  Now  get  a  plank,  siiy 
one  and  a  half  inches,  of  any  thickness  that  may  be 
ag'ced  upon,  the  length  may  be  obtained  by  multiply- 
ing the  longest  side  of  the  pitch-boards,  AC.  Fig.  52, 
by  the  number  of  riser**:  but  as  this  is  the  only  class  of 
stairs  that  the  length  >  Jring-boards  can  be  obtained 
in  this  way  I  would  rer-,  .mend  tb.c  her^inner  to  prac- 
tice the  sure  plan  of  taking  the  pitch-hoard  and  apply- 
ing it  as  at  I,  2.  3,  19,  Fig.  55.     Drawing  all  the  steps 


JOINER'S  WORK 


i6i 


this  way  will  prevent  a  mistake  that  sometimes  occurs, 
viz.  the  string-boards  being  cut  too  short.  Cut  the 
foot  at  the  line  AB,  and  the  top,  as  at  CD.  This  will 
give  about  one  and  a  half  inches  more  than  the 
extreme  length.  Now  cut  out  the  treads  and  risers; 
the  width  of  stair  is,  say,  three  feet,  and  we  have  one 
and  a  half  inches  on  each  side  for  string-boards. 
Allow  three-eights  of  an  inch  for  housing  on  each 
side.  This  will  make  the  length  of  tread  and  risers 
two  and  one-fourth  inches  less  than  the  full  width  of 
stairs;  and  as  the  treads  must  project  their  own  thick- 
ness over  rise,  which  is,  say,  one  and  a  half  inches,  the 
full  size  of  tread  will  be  two  feet  by  eleven  and  one- 
half  inches,  and  of  the  risers  two  feet  nine  and  three- 
fourths  inches  by  six  inches;  and  observe  that  the  first 
riser  will  be  the  thickness  of  the  tread  less  than  the 
others;  it  will  be  only  four  and  one-half  inches  wide. 
The  reason  of  this  riser  being  less  than  the  others  is 
because  it  has  a  tread  thickness  extra. 

I  will  now  leave  the  beginner  to  prepare  all  his  work. 
Dress  the  risers  on  one  face  and  one  edge;  dress  the 
treads  on  one  face  and  both  edges,  making  them  all 
of  equal  width;  gauge  the  ends  and  the  face  edge  to 
the  required  thickness,  and  round  off  the  nosings; 
dress  the  string-boards  to  one  face  and  edge  to  match 
each  other. 

A  plan  of  a  stair  having  13  risers  and  three  winders 
below  is  :hown  at  Fig.  56.  This  shows  how  the  whole 
stair  may  be  laid  out.  It  is  inclosed  between  two 
walls. 

The  beginner  in  stair-work  had  better  resort  to  the 
old  method  of  using  a  story-rod  for  getting  the  num- 
ber of  risers.  Take  a  rod  and  mark  on  it  the  exact 
height  from  top  of  lower  floor  to  top  of  next  floor,  then 


i6a 


MODERN  CARPENTRY 


l\  J 


i 


divide  up  and  mark  off  the  number  of  risers  required. 
There  is   always  one  more  riser  than  trea.l  in  every 
flight  of  stairs.     The  first  risrr  must  be  cut  the  thick- 
ness of  the  tread  less  than  the  others. 
When  there  are  winders,  special  treatment  will  be 

JifflMJ 


LANOINC  , 


Fig.  6()< 


I* 


i 


IS 

IB 

II 

10 

9 

i 

7 

6 

s 

4- 

im^HBi 

^m 

l« 

PL 

AM 

required,  as  shown  in  Fig.  56,  for  the  treads,  but  the 
riser  must  always  be  the  same  width  for  each  separate 
flight. 

When  the  stair  is  straight  and  without  winders,  a 
rod  may  be  used  for  laying  off  the  steps.  The  width 
of  the  steps,  or  treads,  will  be  governed  somewhat  by 
the  space  allotted  for  the  run  of  the  stairs. 

There  is  a  certain  proportion  existing  between  the 
tread  and  riser  of  a  stair,  that  should  be  kept  to  as  close 
as  possible   when    laying   out   the  work       Architects 


JOINER'S   WORK 


163 


say  that  the  exact  measurement  for  a  tread  and  riser 
should  be  sixteen  incli(-s.  or  thereabouts.  That  is,  if  a 
riser  is  made  six  inch(ts,  the  tread  should  be  ten  inches 
wide,  and  so  on.  I  give  a  table  herewith,  showing  the 
rule  generally  made  use  of  by  stair  builders  for  deter- 
mining the  widths  of  risers  and  treads: 


7>tads 

Kitert 

7>eads 

/fistrs 

Inche* 

iDcheit 

Inches 

laches 

5 

9 

12 

5>4 

6 

8^ 

13 

5  , 

7 

8 

14 

4>i 

8 
9 

7'A 
7 

\l 

4 
3H 

10 

6% 

17 

3 

II 

6 

18 

2}i 

It  is  seldom,  however    that  the  proportion  of  the 


riser  and  step  is  exactly  a  matter  of  choice — the  room 


i64 


MODERN  CARPENTRY 


allotted  to  the  stairs  usually  dctermin«'s  this  propor- 
tion; but  the  above  will  be  found  a  useful  standard,  to 
which  it  is  desirable  to  approximate. 

In  better  class  I  uldingi  the  number  of  steps  is  con- 
sidered in  the  plan,  which  it  is  the  business  of  the 
architect  to  arrange,  and  in  such  cases  the  height 
of  the  story-rod  is  simply  divided  to  the  number 
required. 

An  elevation  of  a  stair  with  winders  is  sho^'n  at 
Fig.  57,  where  the  story-rod  is  in  evidence  with  the 
number  of  risers  figured  off. 


Fig.  58  shows  a  portion  of  an  open  string  stair,  with 
a  part  of  the  rail  laid  on  it  at  AB,  CD,  and  the  newel 
cap  with  the  projection  at  A.  This  shows  how  the 
cap  should  stand  over  the  lower  step. 

Fig.  59  shows  the  manner  of  constructing  the  step; 
S  represents  the  string,  R  the  risers,  T  the  tread,  O 
the  nosing  and  cove  moulding,  and  B  is  a  block  glued 
or  otherwise  fastened  to  both  riser  and  tread  to  render 


^ 


JOINERS  WORK 


'65 


them  strong  and  firm.     It  will  be  seen  the  riser  is  let 

in  the  trea'i  and  has  a  shoulder  on  the  insid*-.  The 
bottom  of  th  riser  is  nailed  to  the  back  of  the  next 
!i  wer  tread,  which  binds  the  whoi  lower  part  to- 
gether. The 
nosing  of  the 
stair  is  ^-^cn- 
c  r  a  1  '  y  re- 
turned i  the 
(\)cn  end  of 
the  tread, 
and  this  ■  ov- 
ers the  ' nd 
wo.  (I  of  *he 
tread  anu  the 
joints  of  the 
balusters,  as 
shown  at 
Fif,'.  CiO. 

When  a  stair  is  bracketed,  as  shown  at  B,  Fig.  60, 
I  lie  point  of  the  riser  on   its  strin-,'  r?nd  should  be  left 

vE;.  ifng  past  the  string 
the  thickness  of  the 
bracket,  and  the  end  of 
the  bracket  miters 
against  it,  thus  avoid- 
ing the  necessity  of 
showing  end  wood  or 
joint.  The  cove  should 
finish  inside  the  length 
of  the  bracket,  and  the 
nosing  should  fin- 
ish just  outside  the 
When  brackets  are  employed 


Fig.  60. 


length  of  the  bracket. 


i66 


MODERN   CARPENTRY 


they  should  continue  along  the  cylinder  and  al) 
around  the  well -hole  trimmers,  though  they  may 
be  varied  to  suit  conditions  when  continuously  run- 
ning on  a  straight  horizontal  facia. 


ill 


^ 


1 


3 

J 

^ 


CHAPTER  III 

joiner's  work— useful  miscellaneous  examples 

I  am  well  aware  that  workmen  are  always  on  the 
lookout  for  details  of  work,  and  welcome  everything 
in  this  line  that  is  new.  While  styles  and  shapes 
change  from  year  to  year,  like  fashion  in  women's 
dress,  the  principles  of  construction  never  change, 
and  styles  of  finish  in  woodwork  that  may  be  in  vogue 
to-day,  may  be  old-fashioned  and  discarded  next  year, 
therefore  it  may  not  be  wise  to  load  these  pages  with 
many  examples  of  finish  as  made  use  of  to-day.  A 
few  examples,  however,  may  not  be  out  of  place,  so  I 
close  this  section  by  offering  a  few  pages  of  such 
details  as  I  feel  assured  will  be  found  useful  for  a  long 
time  to  com'. 

full  page  illustration  of  three  exam- 
and  newels  in  modern  styles.  The 
colonial  stairway  with  a  square  newel, 
A  baluster  is  also  shown,  so  that  the 
whole  may  be  copied  if  required.  The  second  exam- 
ple shows  two  newels  and  balusters,  and  paneled  string 
and  spandril  AB,  also  section  of  paneled  work  on  end 
of  short  flight.  The  third  shows  a  plain  open  stair, 
with  baluster  and  newel,  the  latter  starting  from 
first  step. 

At  Fig.  2,  which  is  also  a  full  page,  seven  of  the 
latest  designs  for  doors  are  shown.      Those  marked 

167 


Fig.  I  is  a 
pies  of  stairs 
upper  one  is  a 
as  shown  at  A. 


i 


i68 


MODERN   CARPENTRY 


JOINER'S  WORK 


169 


'I 


Hi 


170 


MODERN   CARPENTRY 


ABCD  are  more  particularly  employed  for  inside 
work,  while  F  and  G  may  be  used  on  outside  work; 
the  five- paneled  door  being  the  more  popular. 

There  are  ten  different  illustrations,  shown  at  Fig.  3, 
of  various  details.  The  five  upper  ones  show  the  gen- 
eral method  of  constructing  and  finishing  a  window 
frame  for  weighted  sash.  The  section  A  shows  a  part 
of  a  wall  intended  for  brick  veneering,  the  upper  story 
being  shingled  or  clapboarded. 

The  position  of  windows  and  method  of  finishing 
bottom  of  frame,  both  inside  and  out,  are  shown  in 
this  section,  also  manner  of  cutting  joists  for  sill. 
The  same  method — on  a  larger  scale — is  shown  at  C, 
only  the  latter  is  intended  for  a  balloon  frame,  which 
is  to  be  boarded  and  sided  on  the  outside. 

At  B  another  method  for  cutting  joists  for  sill  is 
shown,  where  the  frame  is  a  balloon  one.  This  frame 
is  supposed  to  be  boarded  inside  and  out,  and  grounds 
are  planted  on  for  finish,  as  shown  at  the  base.  There 
is  also  shown  a  carpet  strip,  or  quarter-round.  The 
outside  is  finished  with  siding. 

The  two  smaller  sections  show  foundation  walls, 
heights  of  stories,  position  of  windows,  cornices 
and  gutters,  and  methods  of  cornecting  sills  to 
joists. 

A  number  of  examples  are  shown  in  Fig.  4  that  will 
prove  useful.  One  is  an  oval  window  with  keys. 
This  is  often  employed  to  light  vestibules,  back  stairs 
or  narrow  hr.llways.  Another  one,  without  keys,  is 
shown  on  the  lower  part  of  the  page.  There  are  three 
examples  of  eyebrow  dormers  shown.  These  arc 
different  in  style,  and  will,  of  course,  require  different 
construction. 

The  dormer  window,  shown  at  the  foot  of  the  page, 


JOINER'S   WORK 


i7> 


I 


■f| 


)  m 

h 


i 


L„.:  i 


B   S 


17a 


MODERN  CARPENTRY 


ill 


fii^ 


JOINER'S   WORK 


173 


is  designed  for  a  house  built  in  colonial  style,  but  may 
be  adapted  to  other  styles. 

The  four  first  examples  in  Fig.  5  show  the  sections 
of  various  parts  of  a  bay  window  for  a  balloon  frame. 
The  manner  of  constructing  the  angle  is  shown,  also 
the  sill  and  head  of  window,  the  various  parts  and 
manner  of  working  thorn  being  given.  A  part  of  the 
section  of  the  top  of  the  window  is  shown  at  E,  the 
inside  finish  being  purposely  left  off.  At  F  is  shown 
an  angle  of  greater  length,  which  is  sometimes  the 
case  in  bay  windows.  The  manner  of  construction  is 
quite  simple.  The  lower  portion  of  the  page  shows 
some  fine  e.xnmplcs  of  turned  and  carved  work.  These 
will  often  be  found  useful  in  giving  ideas  for  turned 
work  for  a  variety  of  purposes. 

Six  examples  of  shingling  are  shown  in  Fig.  6. 
The  first  sketch,  A,  is  intended  for  a  hip,  and  is  a 
fairly  good  example,  and  if  well  done  will  insure  a 
water-tight  roof  at  that  point.  In  laying  out  the 
shingles  for  this  plan  the  courses  are  managed  as  fol- 
lows: No.  I  is  laid  all  the  way  out  to  the  line  of 
the  hip,  the  edge  of  the  shingle  being  planed  off,  so 
that  course  No.  2,  on  the  adjacent  side  will  line  per- 
fectly tight  down  upon  it.  Next  No.  3  is  laid  and  is 
dressed  down  in  the  sa  ne  manner  as  the  first,  after 
which  No.  4  is  brought  a'ong  the  same  as  No.  2.  The 
work  proceeds  in  this  manner,  first  right  and  then  left. 

In  the  second  sketch,  B,  the  shingles  are  laid  on  the 
hip  in  a  way  to  bring  the  grain  of  the  shingles  more 
nearly  parallel  with  the  line  of  the  hip.  This  method 
overcomes  the  projection  of  cross-grained  points. 
Another  mctiiod  of  shingling  hips  is  shown  at  C  and 
D.  In  putting  on  shingles  by  this  method  a  line  is 
snapped  four  inches  from  angle  of  hip  on  both  sides 


h^fic^- 


»74 


MODERN  CARPENTRY 


rv>^ 


m 


i2i^ 


i.^iram5ii'««&^^^^ 


JOINER'S  WORK 


«TS 


of  the  ridge,  as  indicated  by  the  dotted  lints  in  C,  then 
bring  the  corner  of  the  shingles  of  each  course  to  the 
line  as  shown.  VVht  n  all  through  with  the  plain  shin- 
gling, make  a  pattern  to  suit,  and  only  cut  the  top  to 
shape,  as  the  bottoms  or  butts  will  break  joints  every 
time,  and  the  hip  line  will  lay  square  with  the  hip 
line,  as  shown  at  D;  th-.is  makin,^  a  first-class  water- 
tight job,  and  one  on  which  tlse  shingles  will  not  curl 
up,  and  it  will  have  a  good  appearance  as  well. 

At  E  a  method  is  shown  for  shinglii.g  a  valley, 
where  nc.  tin  or  metil  is  employed.  The  maiv.ier  of 
doing  this  work  is  as  follov.s:  P'irst  take  a  stiip  4 
inches  wide  and  chamfer  it  on  the  rdges  on  i\\'-t  out- 
side, so  that  It  will  lay  down  s.nooth  to  tlu;  sheeting, 
and  nail  it  into  the  valley  Take  a  shin^de  about  4 
inches  w-de  to  start  with  and  lay  lengthwise  of  the 
valley,  fitting  the  shingle  on  each  side.  The  first 
course,  which  is  always  doable,  would  then  start  with 
the  narrow  shingle,  marked  B,  ant!  carried  up  the  val- 
ley, as  shown  in  the  sketch.  Half  way  between  each 
course  lay  a  shingle,  A.  about  4  or  5  inches  wide, 
as  the  case  requires,  chamferin  j  underneath  on 
each  side,  so  that  the  ntxt  course  will  lie  smooth 
over  it. 

If  tin  or  zinc  can  be  obtained,  it  is  better  it  should 
be  laid  in  the  valley,  whether  this  method  be  adopted 
or  not. 

The  sketch  shown  at  F  is  intended  to  illustrate  the 
manner  in  which  a  valley  should  be  laid  with  tin,  zinc 
or  galvanized  iron.  The  dotted  line--:  show  the  width 
of  the  meta'i,  which  &;:ouUi  never  ',  less  than  four- 
teen inches  to  insure  a  tight  roof.  The  shingles 
should  lap  o\er  as  shown,  and  not  less  than  four 
inches  of  the  valley,  H,  should  be  clear  of  shingic". 


m 


176 


MODERN   CARPENTRY 


In  ■' 


*•    "^- 


JOINER'S  WORK 


»77 


in  order  to  insure  plenty  of  space  for  the  water  to 
flow  during  a  heavy  rain  storm.  A  great  deai 
of  care  should  \>c  taken  in  shingling  and  finishing  a 
valley,  as  it  is  always  a  weak  spot  in  the  roof. 


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(ANSI  and  ISO  TEST  CHART  No   2) 


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^Sr.  1653  East   Mam   Street 

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*4Ial   iWIii 


1  f 
'J  I 


I 


PART    IV 


i 


USEFUL   TABLES   AND   MEMORANDA 
FOR   BUILDERS 

Table  showing  quantity  of  material  in  every  four 
lineal  feet  of  exterior  wall  in  a  balloon  frame  build- 
ing, height  of  wall  being  given: 


o 

5. 

<n 

0 
u 

N 

Size  of  Studs, 
Braces,  etc. 

Quantity  of 
Rough  turaber 

Quantity  of 
Incli  Boarding. 

¥. 
•5  ^ 
■7.  M 

P 

a.  a 

8 

OX  0 

2x4  Studs. 

42 

36 

40 

74 

10 

6x  8 

4x4  braces. 

52 

44 

50 

80 

12 

6xio 

4x4  plates. 

62 

53 

60 

96 

14 

6x10 

1x6  ribbons. 

^ 

62 

70 

112 

16 

8x10 

82 

71 

80 

128 

18 

8x10 

studs. 

87 

80 

90 

144 

20 

8x12 

16  inches  from 

q3 

83 

100 

160 

22 

9x12 

centers. 

log 

97 

no 

176 

24 

10x12 

119 
122 

100 

120 

192 

18 

10X10 

2x6  .studs. 

So 

qo 

144 

20 

10X12 

6x6  braces. 

137 

88 

100 

160 

22 

10X12 

4x6  plates. 

145 

Q7 

no 

176 

24 

12X12 

1x6  ribbons. 

162 

106 

120 

192 

26 

10x14 

I6g 

114 

130 

20S 

28 

10x14 

studs  16  inch  centers. 

176 

123 

140 

224 

30 

12x14 

198 

132 

150 

240 

1  !| 


179 


I  So 


MODERN  CARPENTRY 


Table  showing  amount  of  lumber  in  rafters,  collar- 
piece  and  boarding,  and  number  of  shingles  to  four 
lineal  feet  of  roof,  measured  from  eave  to  eave  over 
ridge.     Rafters  l6-ir.ch  centers: 


nil  ■-. 


Quantity  of 

Width 

Size  of 
Collar- 

Lumber 

Quantity 

of 

Size  of 

in  Rafter 

of 

No.  of 

House, 

Rafters. 

and 

Boardini;, 

Shingles. 

Feet. 

Collar- 
piece. 

Feet. 

14 

2x4 

2x4 

39 

61 

560 

16 

2x4 

2x4 

45 

70 

640 

18 

2x4 

2x4 

50 

79 

720 

20 

2x4 

2x4 

56 

83 

Sort 

22 

2x4 

2x4 

62 

97 

8  30 

94 

2x4 

2x4 

67 

106 

960 

20 

2x6 

2x6 

84 

88 

800 

22 

2x6 

2x6 

92 

97 

880 

24 

2x6 

:x6 

101 

106 

960 

26 

2x6 

2x6 

lOg 

ii« 

1040 

28 

2x6 

2x6 

117 

124 

1120 

30 

2x6 

2x6 

126 

J33 

1200 

i; 

i 

I. 

:  ; 

|.i 

.i    i 

l: 

,;i  1 

A  proper  allowance  for  waste   is    included    in  the 
above.     Ro9f,  one-fourth  pitch. 


Table  showing  the  requisite  sizes  of  girders  and 
joists  for  warehouses,  the  span  and  distanc* :  apart 
being  given: 


8*: 

5 

Span  of 

Girders. 

Joists. 

Remarks. 

6  Feet. 

8  Feet. 

10  Feet. 

12  Feet. 

Feet. 
10 
12 
14 

Inches. 
8X12 
9x12 

10x12 

Inches. 
12x13 
12x14 
12x15 

Inches. 
12x16 
I2XlS 
14x18 

Inches. 
1 4X I S 
16x18 

Inches 
2lxio 
3  xio 
3x12 

Girders  to  have  a 
bearinj^    at    each 
end  and  joists  6  in. 

USEFUL   TABLES 


i8i 


etc. 


Table  as  before,  adapted  for  churches,  public  halls, 


Span  of 

GiRDEKS. 

Joists. 

Rtitiarks. 

s< 

8  Feet. 

8  Feet. 

10  Fett. 

I^'  Feet. 

Feet. 
12 

13 
14 
15 
16 

17 

18 

Inches. 

6x10 

9X1 1 

6X12 

7x12 

8x12 

8x12 

9x13 

9x12 

10x12 

10x12 

11x12 

11x12 

10x13 

10x13 

10x14 

10x14 

Inches. 
8X12 
9x12 
IOXI2 
11X12 
12X12 
9X14 
10x14 
11x14 
12x14 
11x15 
12x15 
11x16 
12x16 
12x17 
12x18 
12x18 

Inches. 

12x14 

IIXI5 

12x15 

11x16 

12x16 

12x17 

11x18 

I2ZI8 

13x18 

14x18 

Inches. 

12x16 

12x17 

11x18 

12x16 

13x18 

14x18 

laches. 
2X8 
2x9 
2x9 
2    XIO 
2     XIO 
2     3{12 

2  X12 
2ixi2 
2|  X12 
24x12 

3  X12 
3    XI2 

3   XI3 
3    X13 
3    X14 

3   x?4 

Bearings  of 
girders  and 
joists  as 
above. 

19 

Both  tables 
are  c  a  1  c  u- 
lated  for  yel- 
low pine. 

20 

*"'• 

31 

22 

23 

24 

Sr 

i6 

27 

Table  showing  quantity  of  lumber  in  every  four 
lineal  feet  of  partition,  studs  being  placed  16  centers, 
waste  included: 


Height  of  Partition, 
Feet. 

Quantity  of  studs  2x4 
Feet. 

If  2x9 
Feet. 

8 

20 

30 

9 

23 

34 

10 

36 

38 

II 

29 

42 

13 

32 

46 

»3 

35 

51 

»4 

38 

55 

15 
16 

41 
44 

59 

64 

r 


W 


183 


i.     • 

f     - 


l-i 


'  i 


Hi  '■-  ^  i 


MODERN   CARPENTRY 


Lumber  Measurement  Table 


t 

ji 

JS 

M 

A 

^ 

^ 

It 

"& 

5 

5 

5 

s 

s 

S 

8X4 

2x6 

2x8 

3X1 

3x6 

3x8 

13 

8 

12 

i: 

12 

16 

12 

20 

12 

18 

12 

24 

14 

9 

U 

14 

14 

19 

14 

23 

14 

21 

14 

28 

16 

II 

16 

16 

16 

21 

16 

27 

16 

24 

16 

32 

Itj 

12 

18 

18 

18 

24 

18 

30 

18 

27 

18 

36 

20 

13 

20 

2C 

20 

27 

20 

33 

20 

30 

20 

40 

22 

15 

22 

22 

22 

29 

22 

37 

22 

33 

22 

44 

24 

16 

24 

24 

24 

32 

24 

40 

24 

36 

24 

48 

26 

17 

26 

26 

26 

35 

26 

43 

26 

39 

26 

52 

3x10 

3x12 

4x4 

4x6 

4x8 

6x6 

12 

30 

12 

30 

12 

16 

12 

24 

12 

32 

12 

36 

14 

35 

'4 

42 

14 

19 

14 

28 

14 

37 

14 

42 

16 

40 

16 

48 

16 

21 

16 

32 

i6 

43 

16 

48 

18 

45 

18 

54 

IB 

24 

18 

36 

18 

48 

IS 

54 

20 

50 

20 

60 

20 

27 

20 

40 

20 

53 

20 

60 

22 

55 

32 

f,6 

22 

29 

22 

44 

22 

59 

22 

66 

24 

60 

24 

72 

24 

j2 

24 

48 

24 

64 

24 

72 

26 

<>5 

26 

78 

26 

35 

26 

52 

26 

69 

26 

78 

6xS 

8x8 

8x10 

KIXIO 

10X12 

12X12 

12 

48 

12 

64 

12 

bu 

12 

100 

12 

120 

12 

144 

14 

56 

14 

75 

14 

93 

14 

117 

14 

140 

'4 

168 

16 

64 

16 

«5 

16 

107 

16 

133 

16 

160 

16 

192 

18 

72 

IS 

96 

18 

120 

iS 

150 

18 

180 

18 

216 

20 

80 

20 

10- 

20 

133 

20 

167 

20 

200 

20 

240 

22 

88 

22 

"7 

22 

147 

22 

1S3 

22 

220 

22 

264 

24 

96 

24 

128 

24 

160 

24 

200 

24 

240 

24 

288 

26 

104 

26    ,130 

26 

173 

26 

217 

26 

260 

26 

312 

Strength  of  Materials 

Resistance  to  extension  and  compression,  in  pounds  per  square 
inch  section  of  some  materials. 


Name  of  the 

Resistance 

Resistance 

Teiieile  Stre'th 

Comp.StrenHh 

Material. 

to  Extension. 

to  Compression 

in  Practice. 

in  Practice 

White  pine... 

10,000 

6,000 

2,000 

1,200 

White  oak.... 

15,000 

7,500 

3, 000 

1,500 

Rock  elm 

16,000 

8,011 

3.200 

1,602 

Wroughtiron 

60,000 

50,000 

12,000 

10,000 

Cast  iron 

20,000 

100,000 

4,000 

20,000 

In    practice,    from    one-fifth    to    one-sixth    of    the 
strength  is  all  that  should  be  depended  upon 


USEFUL  TABLES 


183 


Table  of  Superficial  or  Flat  Measure 

By  which  the  contents  in  Superficial  Feet,  of  Boards,  Plank,  Pav- 
ing, etc.,  of  any  Length  and  Breadth,  can  be  obtained,  by 
multiplying  the  decimal  expressed  in  the  Utble  by  the  length 
of  the  board,  etc. 


Breadth 

Ar«a  of  a  lin- 

i^raailth  Area  of  a  liri- 

Braadtn 

Ar«,-    'alin- 

8rt...'th 

Arttof  a  lin- 

Inchat. 

eal  loot. 

ir,che».         a 

al  foot. 

Inchea. 

.,   foot. 

inc'iea. 

eal  foot. 

■ 

.0208 

3 

2708 

61 

.5208 

9i 

.7708 

.0417 

3 

2Ql6 

b\ 

•  5416 

9 

.7917 

i 

.0625 

3 

3125 

6f 

.5625 

9 

.8135 

I 

.0834 

4 

3334 

7 

•5833 

10 

.8334 

I  ■ 

.1042 

4 

3542 

71 

.6042 

10 

.8542 

I 

.125 

4 

375 

71 

.62r 

10 

.875 

' 

•  1459 

4 

3953 

7i 

.6458 

10 

•8959 

2 

.1667 

5 

4167 

8 

.6667 

I 

.9167 

2i 

.1S75 

51 

4375 

«i 

.6875 

"1 

•9375 

H 

.2084 

5i 

45S3 

«i 

.7084 

I'i 

.958- 

n 

.2292 

5S 

4792 

bl 

.7292 

"S 

•9 

3 

•25 

6 

5 

9 

•75 

12 

T 

Round  and  Equal-Sided  Timber  Measure 
Table  for  ascertaining  the  number  of  Cubical  Feet,  or  solid  con- 
\.    tents,  in  a  Stick  of  Round  or  Equal-Sided  Timber,  Tree,  etc. 


Mgirt 

Area  In 

Mgirt 

Area  in 

ygirt 

Area  in 

'^Rit 

A-er  in 

H  gi't 

Area  in 

in  in. 

feet. 

in  in. 

feet. 

in  in. 

feet. 

In  If). 

feet. 

in  in. 

feet. 

6 

•25 

loj      .803 

I5i 

1.668 

20 1 

2.898 

25 

4.34 

bi 

.272 

II           .84 

»5J 

1.722 

2o| 

2.917 

25} 

4.428 

64 

.294 

III        .878 

10 

1.777 

20 1 

2.99 

25i 

4.516 

6J 

.317 

Il|        .9IS 

I6i 

1-833 

21 

1      "^7 

25? 

4.605 

7 

•34 

II»        .959 

161 

1.89 

2li 

26 

4.694 

7 

•3f4 

12       I. 

165 

1.948 

214 

^.-uq 

26 

4.785 

7 

•39 

12        1.042 

17 

2.005 

213 

3285 

26 

4.876 

r 

•417 

12        1.085 

I /I 

2.066 

22 

3.362 

26 

4-969 

8 

•444 

12        1. 129 

I7i 

2.  I  26 

22J 

3-438 

27 

5-062 

8 

.472 

13      I.I74 

I7i 

2.187 

22| 

3-516 

271 

5-158 

8 

.501 

I3i    1219 

18 

2.25 

22} 

3-598 

27i 

5- 252 

8i 

.531 

I3J     1.265 

isi 

£•313 

23 

3.673 

271 

5-348 

9 

.562 

I3l    1-313 

78f 

2.376 

231 

3-754 

28 

5-444 

9l 

.594 

14      1361 

l^ 

2.442 

23i 

r835 

28i 

5-542 

9^ 

.626 

I4i    I.4T 

19 

2.506 

23J 

3917 

28. 

5.64 

93 

.6^9 

I4i    l.4>' 

I9l 

2-574 

24 

4 

285 

5-74 

10 

.'n» 

m|    ^  5'I 

'9i 

2  64 

"41 

40R4 

29 

5.84 

lOl 

•73 

15      1-562 

193 

2.709 

24!' 

4.168 

294 
29J 

5.94  s 

104 

.766 

I5>    1. 615 

20 

2-777 

241 

4.254 

6.044 

Ill 


184 


MODERN   CARPENTRY 


Shingling 

To  find  the  niimberof  shingles  required  to  cover  ICX) 
square  feet  deduct  3  inches  from  the  length,  divide 
the  remainder  by  3,  the  result  will  be  the  exposed 
length  of  a  shingle;  multiplying  this  with  the  average 
width  of  a  shingle,  the  product  will  be  the  exposed 
area.  Dividing  14,400,  the  number  of  square  inches 
in  a  square,  by  the  exposed  area  of  a  shingle  will  give 
the  number  required  to  cover  100  square  feet  of  roof. 

In  estimating  the  number  of  shingles  required,  an 
allowance  should  always  be  made  for  waste. 

Estimates  on  cost  of  shingle  roofs  are  usually  given 
per  1,000  shingles. 

Table  for  Estimating  Shingles 


Length  of 
SLiagles. 

Bxposure  to 
Weather, 
Inches. 

No.  of  Sq.  Ft.  of  Roof  Cov- 
ered by  lUOO  Shingles. 

No  of  Shingles  Required 
for  100  Sq.  Ft.  of  Roof. 

4  In.  Wide. 

6  In.  Wide. 

4  In.  Wide. 

6  In.  Wide. 

15  in. 

18 
31 
24 
27 

4 
5 

6 

7 

8 

Ill 

139 
167 
194 
222 

167 

208 
250 
291 

3.33 

900 
720 
600 
514 
450 

600 
480 
400 

343 
300 

Siding,  Flooring,  and  Laths 

One-fifth  more  siding  and  flooring  is  needed  than 
the  number  of  square  feet  of  surface  to  be  covered, 
because  of  the  lap  in  the  siding  matching. 

1,000  laths  will  cover  70  yards  of  surface,  and  11 
pounds  of  lath  nails  will  nail  them  on.  Eight  bushels  of 
good  lime,  16  bushels  of  sand,  and  i  bushel  of  hair, 
will  make  enough  good  mortar  to  plaster  100  square 
yards. 

Excavations 

Excavations  are  measured  by  the  yard  {2^  cubic  feet) 
and  irregular  depths  or  surfaces  are  generally  averaged 
in  practice. 


USEFUL  TABLES 


185 


Number  of  Nails  Required  in  Carpentry  Work 

To  case  and  hanj^  one  door,  i  pound. 

To  case  and  hang  one  window,  ^  pound. 

Base,  100  lineal  feet,  I  pound. 

To  put  on  rafters,  joists,  etc.,  3  pounds  to  1,000  feet 

To  put  up  studding,  same. 

To  lay  a  6-inch  pine  fluor,  15  pounds  to  1,000  feet. 


I 


Sizes  of  Boxes  for  Different  Measures 

A  box  24  inches  long  by  16  inches  wide,  and 
28  inches  deep  will  contain  a  barrel,  or  3  bushels. 

A  box  24  inches  long  by  16  inches  wide,  and 
14  inches  deep  will  contain  half  a  barrel. 

A  box  16  inches  square  and  8f  inches  deep,  will 
contain  i  bushel. 

A  box  16  inches  by  8|  inches  wide  and  8  inches 
deep,  will  contain  half  a  bushel. 

A  box  8  inches  by  8|  inches  square  and  8  inches 
f^cc  >,  will  contain  I  peck. 

jox  8   inches  by  8  inches  square  and  4|  inches 
wi  1  contain  I  gallon. 

.V  be  8  inches  by  4  inches  square  and  4^  inches 
deep,  wi.l  contain  half  a  gallon. 

A  box  4  inches  by  4  inches  square  and  4J  inches 
deep,  will  contain  i  quart. 

A  box  4  feet  long,  3  feet  5  inches  wide,  and  2  feet 
8  inches  deep,  will  contain  i  ton  of  coal. 

Masonry 

Stone  masonry  is  measured  by  two  systems,  quarry- 
man's  and  mason's  measurements. 


wm 


•HI 


il 


'H 


ti   1 


J. 


1 86 


MODERN  CARPENTRY 


By  the  quarryman's  measurements  the  actual  con- 
tents aie  measured -that  is,  all  openings  are  taken 
out  and  all  corners  .u.-  measured  single. 

V.y  the  mason's  measurements,  corners  and  piers  are 
doubled,  and  no  allovvance  made  for  openings  less 
than  3'o"x5'o"  and  only  half  the  amount  of  openings 
larger  than  3'o"x5'o". 

Range  work  and  cut  work  is  measured  superficially 
and  in  addition  to  wall  measurement. 

An  average  of  six  bushels  of  sand  and  cement  per 
perch  of  rubble  masonry. 

Stone  walls  are  measured  by  the  perrh  (243/^  cubic 
feet,  or  by  the  cord  of  128  feelj.  Openings  I -ss  than 
3  feet  wide  arc  counted  solid;  over  3  feet  deducted, 
but  18  inches  are  added  to  the  running  measure  for 
each  jamb  built. 

Arches  are  counted  solid  from  their  spring.  Corners 
of  buildings  are  measured  twice.  Pillars  less  than 
3  feet  are  counted  on  3  sides  as  lineal,  multiplied  by 
fourth  side  and  depth. 

It  is  customary  to  measure  all  foundation  and  dimen- 
sion stone  by  the  cubic  foot.  Water  tables  and  base 
courses  by  lineal  feet.  All  sills  and  lintels  or  ashlar 
by  superficial  feet,  and  no  wall  less  than  18  inches 
thick. 

The  height  of  brick  or  stone  piers  should  not  exceed 
12  times  their  thickness  at  the  base. 

Masonry  is  usually  measured  by  the  perch  (contain- 
ing 24.75  cubic  feet),  but  in  practice  25  cubic  feet  are 
considered  a  perch  of  masonry. 

Concreting  is  usuallv  measured  by  the  cubic  yard 
(27  cubic  feet). 


ir  f 


..'-'-^ . 


■'I  rOdi 


,■"'■■•♦■ 


«■ 


IT 

I 


''I 


USEFUL  TABLES 


187 


A  cord  of  stone,  3  bushels  of  lime  and  a  cubic  yard 
of  sand,  will  lay  100  cubic  feet  of  wall. 

Cement,  l  bu^ihel,  and  sand,  2  bushels,  will  cover 
il4  square  yards  i  nch  thick,  4'yi  square  yards  }i  inch 
thick,  and  6^  square  yards  "^  inch  thick;  i  bushel  of 
cement  and  I  of  sand  will  cover  2^  square  yards 
1  inch  thick,  3  square  yards  J^  inch  thick  and 
4J.-  square  yards  }4  inch  thick. 


Brick  Work 

Brick  work  is  generally  measured  by  1,000  bricks 
laid  in  the  wall.  In  consequence  of  variations  in  size 
of  bricks,  no  rule  for  volume  of  laid  brick  can  he 
exact.    The  following  scale  is,  however,  a  fair  average' 

7  com.  bricks  to  a  super,  ft.    4  in.  wall. 

I^     ••  •!  ••  <<        ••      „   ■•        •• 

21         **  **  («  *t  n       jn     tl  II 

a8     "         "        "        "      "    18  "      " 

«r      **  **  't  I*        **     22    *'         ** 

Corners  are  not  measured  twice,  as  in  stone  work. 
O  'ings  over  2  feet  square  are  deducted.  Arches  are 
co>  .fvl  from  the  spring.  Fancy  work  counted  i^ 
bricks  for  i.     Pillars  are  measured  on  their  face  only. 

A  cubic  yard  of  mortar  requires  I  cubic  yard  of  sand 
and  9  bushels  of  lime,  and  will  fill  30  hods. 

One  thousand  bricks  closely  stacked  occupy  about 
56  cubic  feet. 

One  thousand  old  bricks,  cleaned  and  loosely 
stacked,  occupy  about  72  cubic  feet. 

One  superficial  foot  of  gauged  arches  requires 
10  bricks. 

Pavements,  according  to  f  ize  of  bricks,  take  38  brick 
on  fiat  and  60  brick  on  edge  per  square  yard,  on  aa 
average. 


t. 


nr^ 


'U 

'  i  I 

n 


II  ' 


:|| 


1 88 


MODERN   CARPENTRY 


Five  courses  of  brick  will  lay  i  foot  in  height  on  a 
chimney,  6  bricks  in  a  course  will  make  a  flue  .\  inches 
wide  and  12  inches  long,  and  8  bricks  in  a  course  will 
make  a  flue  8  inches  wide  and  16  inches  long. 

Slating 

A  square  of  slate  or  slating  is  100  superficial  feet. 

In  measuring',  the  width  of  eaves  is  allowed  at  the 
widest  part.  Hips,  vali.  ys  and  cuttings  are  to  be 
measured  lineal,  and  6  inches  extra  is  allowed. 

The  thickness  of  slates  required  is  from  {g  to  ^'j  of 
at.  =nch.  and  their  weight  varies  when  lapped  from  j| 
to  bf4  pounds  per  square  foot. 

The  "laps"  of  slates  vary  from  2  to  4  inches,  the 
standard  assumed  to  be  3  inches. 


I.'t 


To  Compute  the  Number  of  Slates  of  a  Given 
Size  Required  per  Square 

Subtract  3  inches  from  the  length  of  the  slate,  mul- 
tiply the  remainder  by  the  width  and  divide  by  2. 
Divide  14,400  by  the  number  so  found  and  the  result 
will  be  the  number  of  slates  required. 

Tablr.  showing  number  of  slates  and  pounds  01  nails 
required  to  cover  100  square  feet  of  roof. 


Size*  of  Slate      li.ength  of  Expof-r;. 


14  ill.  X  28  in. 

13    X  24 
II     X  33 

10    X  30 

g   X  18 
v   X  16 

7   t  M 
6   X  12 

i  '-vwr 


'^"^^^wmmss^m^limx^ 


USEFUL   TABLES  ,89 

Approximate  Weight  of  Material!  for  Roofe 


Material 


CorniKatefl  Ralvanized  iron.  No.  20,  unboarfltd. 

fi'plifr,  16  i)z.  starniing  scam 

I>  t  and  asphalt,  witho'it  sheathing 

niass.  J^  in,  thick 

UenilfM  i;  sheathing,  i  in.  tliick 

I.ead,  atmut  '<j  in.  thick 

I-atl)-and-[)!aster  ceiling  (ordinary) 

Mackite,  t  in.  thick,  with  plaster 

Ncjxjnset  roofing  fe't,  a  layers 

Spruce  sheathitig,  i  in.  thick. 


Slate 


ill.  thick,  3  in. 


jble  lap 

Slate,  1^  in.  thick,  3  in.     juble  lap 

Shingles,  6  1n.  xi8in.,   J^' to  weather 

Skylight  of  glass,  ,»,  to  %  in.,  including  frame 

Slag  rtx)'  4-plv 

Terne  Plate,  fC,  without  sheathing !....."!..!!!.! 

Terne  Plate,  IX.  without  sheathing 

Tiles  (plain),  loH  in.  x6'^  x  %  in  — 5^'  in.  to  weather. 
Tiles  (Spanish)  i4<^in.  x  loj^in.  -7'^  in.  to  weather, 

White-pine  sheathing,  i  in.  thick 

Yellow-pine  sheathing,  i  in.  thick ". ." \ 


Average 
WeJRhi   I,b. 
per  Sq  Ft. 


3 

iH 

3 

6  to  8 
6to8 
10 

H 
a>i 

a 

4  to  10 
4 
% 

H 

18 

4 


Saow  and  Wind  L^   -^s 

Data  in  regard  to  snow  and  wind  loads  are  nf     '>sary 
in  connection  with  the  design  of  roof  trii'ise^ . 

Snow  Load. — When  the  slope  of  p  roof  is  over 
12  inches  rise  per  foot  of  h  ontal  ru  .  a  snow  and 
accidental  load  of  8  pounds  p^..  square  foot  is  ample. 
When  the  slope  is  under  12  inches  rise  per  foot  of  run 
a  snow  and  accidental  load  of  12  pounds  per  square 
foot  should  be  used.  The  snow  load  acts  vertically, 
and  therefore  should  be  added  to  the  dead  lead  in 
designing  roof  trusses.  The  snow  load  may  be 
neglected  when  a  high  wind  pressure  has  been  consid- 
ered, as  .T  great  wind  storm  would  very  likely  remove 
all  the  snow  frotr.  the  roof. 


.^'•'^vl'.l 


I90  MODERN  CARPENTRY 

Wind  Load.— The  wind  is  considered  as  blowing  in 
a  horizontal  direction,  but  the  resulting  pressure  upon 
the  roof  is  always  taken  normal  (at  right  angles)  to 
the  slope.  The  wind  pressure  against  a  vertical  plane 
depends  on  the  velocity  of  the  wind,  and,  as  ascer- 
tained by  the  United  States  Signal  Service  at  Mount 
Washington,  N.  H.,  is  as  follows: 

Velocity.  Pressure. 

(Mi.  per  Hr.)  (I,b.  per  Sq.   Ft.) 

'° 0.4 Fresh  breeze. 

"o I  <^ Stiff  breeze. 

30 3  <> Strong  wind. 

40 6.4 High  wind. 

50 lo.o Storm. 

°° 14-4 Violent  stonn. 

^° 25.6 Hurricane. 

^°° 40.0 Violent  hurricane. 

The  wind  pressure  upon  a  cylindrical  surface  is  one- 
half  that  upon  a  flat  surface  of  the  same  height  and 
width. 

Since  the  wind  is  considered  as  traveling  in  a  hori- 
zontal direction,  it  is  evident  that  the  more  nearly 
vertical  the  slope  of  the  roof,  the  greater  will  be  the 
pressure,  and  the  more  nearly  horizontal  the  slope,  the 
less  will  be  the  pressure.  The  following  tabic  gives 
the  pressure  exerted  upon  roofs  of  different  slopes,  by 
a  wind  pressure  of  40  pounds  per  square  foot  on  a 
vertical  plane,  which  is  equivalent  in  intensity  to  a 
violent  hurricane. 

UNITED  STATES  WEIGHTS  AND  MEASURES 
Land  Measure 

I  sq.  acre  =    10  sq.  chains  =  100,000  sq.  links  =  6,272,640  sq.  in. 
I  "       "     =  160  sq.  rods     =       4,840  sq.  yds.  =       43,560  sq.  ft, 
AW^.— 2oS.  7103  feet  square,  or  69. 5701  yards  square,  or  220  feet 
by  198  feet  Bquare=i  acre. 


USEFUL  TABLES 


191 


Cubic  or  Solid  Measure 

1  cubic  yard  =  27  cubic  feet 

1  cubic    foot  =  1,728  cubic  inches. 

I  cubic    foot  =  2,200  cylindrical  inches. 

I  cubic    foot  =  3,300  spherical  inches. 

I  cubic    foot  =  6,600  conical  inches. 


t2 


Linear  Measure 

inches  (in.) =  i  foot ft. 

3    feet =  I  yard yd. 

5. 5  yards =  i  rod rd. 

40    rods =  I  furlong fur. 

8    furlongs  =  i  mile mi. 


in.  ft.  yd. 

36=  3     =  I 

198  =  16.5  =  5- 

7,920  =  660     =  220 


rd.     fur.    mi. 


5  =      I 

=    40  =  I 


63,360=5,280     =1,760     =  320  =  i 


Square  Measure 

144      square  inches  (sq.  in.)  :=  i  square  fix)t sq.  ft. 

9      square  feet =:  I  stiuare  yard  sq.  yd. 

30J    square  yards =  i  square  rod sq.  rd. 

160      square  rods  =  i  acre A. 

640     acres =  i  square  mile sq.  mi. 

Sq.  mi.     A.      Sq.  rd.        Sq.  yd.  Sq.  ft.  Sq.  in. 

I  =  640  =  102,400  =  3.097,600  =  27,878,400  =  4,014,489,600 


M 
¥. 


Miscellaneous  Measures  and  Weights 

I  perch  of  stone  =  i  ft.  X  i  ft.  6  in.  X  16  ft.  6  in.  =  24. 75  ft.  cubic. 

I  cord  of  wood,  clay,  etc.,  =  4  ft.  X  4  ft.  X  8  ft.  =  128  ft.  cubic. 

I  chaldron  =  36  bushels  or  57.25  ft.  cv.bic. 

I  cubit  foot  of  sand,  solid,  weighs  112J  lbs. 

I  cubic  foot  of  sand,  loose,  weighs  95  lbs. 

I  cubic  foot  of  earth,  loose,  weighs  93}  lbs. 

I  cubic  foot  of  common  soil  weighs  1 24  lbs. 

I  cubic  foot  of  strong  soil  weighs  127  lbs. 

I  cubic  foot  of  clay  weighs  120  to  135  lbs. 

I  cubic  foot  of  clay  and  stone  weighs  160  lbs. 

I  cubic  foot  of  common  stone  weighs  160  lbs. 

I  cubic  foot  of  brick  weighs  95  to  1 20  lbs. 

I  cubic  foot  of  granite  weighs  169  to  180  lbs. 

I  cubic  foot  of  marble  weighs  166  to  170  lbs. 

I  cubic  yard  of  .sand  weighs  3,037  lbs. 

I  cubic  yard  of  common  soil  weighs  3,429  lbs. 


«9« 


MODERN   CARPENTRY 


Safe  Bearing  Loads 


m 


\  :> 


Brick  and  Stone  Masonry. 


Bricks,  hard,  laid  in  lime  mortar 

Hard,  laid  in  Portland  cement  mortar 

Hard,  laid  in  Rosendale  cement  mortar...!., 

_,       .                             Masonry. 
Granite,  capstone 

Squared  stonework 

Sandstone,  capstone !."!!!."!!!!!!!]!] 

Squared  stonework ."!.......'.... 

Rubble  stonework,  laidin'iime'morta'r 

Kubble  stonework,  laid  in  cement  mortar"" 
1-imestone,  capstone 

Squared  stonework !.".".".."!......""] 

Rubble,  laid  in  lime  mortar!!.."!!!!... 

Rubble,  laid  in  cement  mortar 

Concrete,  i  Portland.  2  sand.  5  broken"stone! 


Lb.  per 
Sq.  III. 


Foundation  Soils 


Rock,  hardest  in  native  bed 

Equal  to  best  ashlar  masonr\' 

Equal  to  best  brick 

Clay,  drj',  in  thick  beds...!!! 

Moderately  dry,  in  thick"  beds 

Soft 

Gravel  and  course  sand,"wen"ceniented' 
band,  compact  and  well  cemented 

Clean,  dry 

Quicksand,  alluvial'  soir'etr 


100 
200 
150 

700 

3ro 
350 

175 
80 
150 
500 
250 
80 
150 
150 


Tons 
per  Sq.  Ft. 

100  — 

25-40 

15-20 

4-   6 

2-  4 

1-  2 
8-10 
4-  6 

2-  4 
.5-  I 


Capacity  of  Cisterns  for  Each  10  Inches  in  Depth 

Twenty-five  feet  in  diameter  holds  ,„  „ 

Twenty  feet  in  diameter  holds...... f^Q  Ra  ons 

Fifteen  feet  in  diameter  holds  ^^8  ga  ons 

Fourteen  feet  in  diameter  holds noigaLons 

Thirteen  feet  in  diameter  holds 950  ga  ons 

Twelve  feet  in  diameter  holds    ^^  g^  Ions 

Eleven  feet  in  diameter  holds "°5  ^    ' 

Ten  feet  in  diameter  holds     ^92  g 

Nine  feet  in  diameter  holvis "^  ?  ^"m 

Eight  feet  in  diameter  holds 396  gail-ns 

Seven  feet  in  diameter  hoMs ^i    gallons 

Six  and  one-half  feet  in  diameVer"holV's "^"^1  gallons 

Six  feet  in  diameter  holds  206  gallons 

Five  feet  in  di.unetLr  ho]!]" >76  gallons 

Four  and  one-half  feet  in  diameter  Isolds!!!!!!!!!!!!!!!!!!!!  '^^  gl|^^^ 


ons 
Ions 
'ons 


USEFUL  TABLES 


»93 


Poor  feet  in  diamet  ;r  holds 78  gallons 

Three  feet  in  diameter  holds 44  gallons 

Two  and  one-faalf  feet  in  diameter  holds 30  gallons 

Two  feet  in  diameter  holds ig  gallons 

Number  of  Nails  and  Tacks  per  Psund 

NAILS.  No. 

Name.  Size.  per  lb. 

3  penny,  fine  i  J^  inch  760  nails 


3 
4 
5 
6 

7 

8 

9 
10 
12 
16 
20 
30 
40 
50 
6 
8 

10 
12 


'•  i>^ 

"  ^H 

"  2hi 

"  aX 

"  2/2 

"  2^ 

"  3 

"  3H 

"  3K 

"  4 

"  4'X 

"  5 

"  s'A 

' '  fence  3 

"  "    3 

"  "    3H 


480 
300 
200 
160 
12S 

Q2 

72 
60 

44 

32 
24 

iS 

14 
12 

80 
50 
34 
29 


Name. 

1  oz., 

1/2". 

2  ". 


TACKS. 

Length. 
.^        inch., 
.316      "    ■ 


3 
4 
6 
8 

10 
12 

14 
16 
18 
20 
22 
24 


.5-1') 

■■y» 
.7-16 

.q-l6 

■H 
.11-16 

.13-16 

■H 

.15-16 

.1 

.1  1-16 


No. 

per  lb. 

I6,ooi) 

10,666 

8,(x>o 

6,400 

5.333 

4,000 

2,666 

2,000 

1,600 

1.333 

1. 143 

1,000 

888 

800 

727 

666 


Wind  Pressures  on  Roofs 

(Pounds  per  Square  Foot.) 


Rite,  lnch*>  per 
Foot  of  Run, 


4 
6 

8 

13 

16 
18 
24 


Angle  with 
Horizontal. 


1 8'^ 

26' 

33" 

45" 

53° 

56° 

63° 


25' 

33' 

41' 

o' 

7' 
20' 

27' 


Pitch. 
Proportion  of 
Ri«e  to  Span. 


Wind  Preieure, 
Normal  to  Slop*. 


16.8 

23-7 
29.1 
36.1 
38.7 
39-3 
40.0 


In  addition  to  wind  and  snow  loads  upon  roofs,  the 
weight  of  the  principals  or  roof  trusses,  including  the 
other  features  of  the  construction,  should  be  figured  in 
the  estimate.  For  light  roofs,  having  a  span  of  not 
over  50  feet,  and  not  required  to  support  any  ceiling, 
the  weight  of  the  steel  construction  may  be  taken  at 
5  pounds  per  square  foot;  for  greater  spans,  i  pound 
per  square  fool  should  be  added  for  each  10  feet 
increase  in  the  span. 


HOUSE   PLAN   ST^PPLEMENT 


PERSPKCTIVK    VIKWS 
AND     FLOOR    PLANS 


OF 


Twenty-Five    Low  and 
Medium  Priced  Houses 


Full  a,  !  Cmple;  ■  W.irking  Plans  and  Sprcirications  of  anv  „t 
thrse  hi.u.is  will  l,e  mailed  at  th^  l.,w  priirs  named,  .m  the  ^ame 
day  the  order  is  r-ieised. 


OTHER     PLANS 

W.  illustrate  in  'Modern  Carpentry;"  "Practical  I'ses  of  the 
Steel  Square,  Vol.  II;  an,:  "Common  Sense  Hand  Raiiing;" 
-J  other  plans,  -,-  in  each  book,  none  of  which  .-re  duplicates  of 
tnosc  we  illi:,.trate  herein, 

Kor  further  information,  address 

The     PlHLISHF.RS 


S,na  All  Ordtii  for  Plans  to 

RADFORD    ARCHITECTURAL 
COMPANY 


CHIC.iGn,    n./.I.XolS:    n^j  ff,<t  -jJSnret 
RirKRMDi:,    ll.l.l\Oly..    (-;,,,,„  ^/„^ 


m 


if 


■  '1 


h    n 


k 


25    HOUSE,  DESIGNS    25 

WillK.iit  extn  cost  I.,  "ur  rea.lers,  vvi-  Iim'c  ,i.1.1.mI  to  \h:'  xuUvw 
,he  iMTsiHTliv.'  view  and  Hour  plans  ..l  twenty  U^-  low  au.l  mumIium, 
urued  houses,  such  as  !H»  |km-  (rnt.  of  the  home  Imihlers  to-.lay  wish  to 
l,,il.l  In  the  .IrawinfJ  of  the-e  plans  -pceial  elTo,t  has  been  nnole  to 
provhle  for  the  most  e.Mmo.nirM  eonslnftion.  thereby  fl.vmjT  tJ.e  home 
In.ihler  an.l  the  eontraef.r  the  henelit  of  the  savin«  of  n.any  .InUars. 
fur  i..  no  ease  have  we  p.t  any  useless  expense  upon  the  l-uihlmj:. 
sin.plv  to  earrv  out  s.,:ue  pe^  ule  >.  livery  plan  illustrate,!  wtll  show 
l,v  the  complete  workinj:  pi ms  ami  sper,«ication.  .  .t  we  -ive  you  de- 
si.M.s  that  will  work  out  to -he  1, est  aavant,..e  ami  wilUue  you  tl|e  most 

f,;;  your  .m.tiey;  l.esnles.  every  Lit  of  sp  xe  has  l-eeu  ufh/cl  to  the  hest 

advaiitane.  ,.  ,     ,  , 

This  supi.letnent.  as  well  as  all  other  Looks  pul.hshe.l  l>y  t.us  co.n- 
p.,nv  has  for  its  foundation  the  l.est  equipped  ar<'hitectural  estahhsh- 
n.ent  ever  maintaine.l  for  the  purpose  of  furni.hins  'I'e  l>u!."c  \vith 
complete  workinc  plans  and  specdira- 
tioiis  at  the  remarkably  low  jiriceof  oidy 
§•>  III)  per   set.       Mvery  i)lan  is  <U'si>:ned 

hy  a  license.l   architect,    who   stamls  at  -vrx^     /  ^^      > 

the  head  of  his  |.rofessi(in  in  thi-  particu-  r-*    ^        '^^ 

lar  class  of  work.      The    Kadfonl    Houses 
are  now  heinii  erected  in  every  .•omitry 

„f  the  worUl  where  frame  houses  are  built .  whi.'h  bespeaks  f„r  our  plans 
more  than  anythins  we  can  say. 

What  We  Give  You 

The  first  .piestion  vou  will  ask  is,  •■What  do  we  pet  in  ;hese  con>plete 
w,.rki..s;  l.latis  and  specilicat  ions'  Of  what  do  tliey  con.s.st  ?  .Me 
they  the  cheap,  printed  plans  on  tissue  paper  without  delad..  or  speci- 

''\vedonot  blame  vou  for  wishing  to  know  what  you  will  ilri  for 
vour  tnonev.  The  plans  we  sen.l  out  are  the  regtilar  blue-printed  plans 
drawn  one-iuarter  inch  scale  to  the  foot,  showing  all  the  elevations, 
floor  plans  and  =iece^s;,ry  inu-rior  details  We  use  the  very  best  quality 
heavv  (lalha  Blue  Print  I'aper.  number  lODO-X.  using  great  care  ni 
the  blue-printing  to  have  every  line  ami  hgure  perfect  ami  distinct. 


/-*>-! 


-jT  ;■  ■:  i4'/4."; 


I 


What  We  Furnish  In  Blue  Prints 

Foundation  and  Cellar  Plan 

Tllis  MM...(  .shows  th.-  si,.,,,,,  ,,„„|  ,i^,.  „f  ,,||  „..,||^    |,j,.^^^  f,„,ti„j;s.  ,,„s,.s, 


elc,  and  of  wlial  niMtc 


n.'.s  ||„.y  .„■,.  ,.oi,>tiiic|,.,l;  sl,<HVS  111-  loivilioii  of 


•ill  windows,  doors,  rl,i„:,„.y>,  ash  |,i,s.  partitions  and  .|„.  like  Th.- 
d.ff.T..nt  wall  s,.,.tio,.s  ...  niv,.,,.  s|,..wi,t«  th.-ir  .'-.nst  nation  and 
liipasurcinpiits  from  all  the  dilTcicit  points 

Floor  Plans 

These  pl,,„s  show  the  .shape  and  si.e  o.  all  roo,„s,  halls,  and  closets- 
the  loeat.on  and  size  ,>f  all  .loors  an,|  windows;  , he  position  of  all  phind,. 
inK  fixtures,  ^as  lights,  retfiMers.  pa.ury  work,  elc,  ai.d  all  Ihe  nieas,„e. 
nients  that  are  necess.aiy  are  f;iv«'n. 

Elevr>tions 

.V  front,  riKht.  left  an,l  rear  elevation  ate  fnrnished  with  all  the  plans 
Ihese   .Irawtn^rs   are   eotnple.e   and   a.rnra'      i„   everv    respert       Thev 

show  the  shape,  s,ze  an.l  location  of  all  doors  and  window^    vlu- 

rorn.ees,  towers,  l..,ys  a.id  the  like,  at.d.  in  faet.  «,.,e  von  an  exaet  seale 
I'letnre  of  the  h.ni.se  as  it  shonid  he  .t  eon,plet,o„.  r„|l  ,..,|1  sertion- 
are  pven.  s1,owh.«  tl,e  ■•onstrueiio,,  on,  foundation  to  ro,  the  Lei-dit 
of -stones  between  the  joists.  l,ei;;ht  of  plates.  p,„.h  of  r.,of,  ,!,.. 

Roof  Plan 

This  plan  is  fnrnishe<l  where  the  rfiof 
eonsli-iiction  isat  allimricate.  It  shows  the 
location  of  all  hijis,  valleys,  ridjres,  decks,  etc. 

■Ml  tiie  above  drawings  are  made  to 
scale  oric-.|ii,arter  inch  to  the   foot. 

Details 

All  ne...ssary  details  of  the  interior  work, 
such  as  door  and  window  casings  and 
trim,  base,  stools,  pictni-e  nionldinir,  do„rs. 
newel  posts,  bMhislers.  rail,  etc.,  accompaiiv 
each  set  of  plan.s.  Part  is  shown  in  full 
size,  while  .some  of  the  lar-er  work,  such 
as  stair  con.st ruction,  is  drawn  to  a  seale 
of  one  and  one-half  inch  to  the  foot. 

These  bltit-  print.s  are  Mib.-,taritiaiiv  and 
arli.stieally  bound  in  cloth  and  heavy  water- 
l>r<.of  paper,  making  a  handsome  ami  dur- 
able covering  and  prolectiMii  for  the  i)lans. 


3 


Specifications 

llic  s|(»'cilicnliiiii.s  arc  typfAiitlfii  (in 
I,ak«'jiii|p  lii>tiil  l.iiiiMi  Paper  ami  arc  Ixiiiiul 
ill  lliP  saiiH-  artistic  iiiamicr  asllic  pla.is,  the 
same  {■\n\U  ami  «:itcrpr(">f  papci  licii<i;  iiscil. 
'I'licv  cim  isl  <p|  friiiii  aliipiit  sivtccii  to  twenty 
jiap-s  iif  cidsciy  typcwriltcii  tiiatter,  (I'viiiK 
full  iiisiriictiiiii-i  fi)i  <'ariyiti):  mil  tlicwDrk. 
All  ilircctiiitis  iic(c>sMry  are  ii\\vn  in  the 
clearest  atid  must  explicit  iiiMiiiier.  so  that 
there  can  lie  no  pussilnlitN  of  a  misiiiuler- 
siaridimi. 


\: 


Basis  of  Contract 

These  .\orkiii«  plans  ami  speciticalions  cati  lie  made  the  liasis  ot 
contract  lietween  the  home  Kuilder  and  the  contracior.  They  will 
prevent  mistakes  which  cost  money,  and 
thev  will  pfcxcnl  disputes  which  are  unfore- 
seen and  ncMM- settled  satisfactorily  to  tiolh 
parties  Ulicti  no  plans  are  used,  t  he  coii- 
tractoi  is  often  oliliire<l  to  do  some  work 
which  he  did  not  fi^nire  on,  and  the  home 
builder  often  docs  not  jict  as  much  for  his 
tioney  as  he  c\pei-tc  I.  simply  hecausc  there 
was  no  hasi"!  on  which  to  work  and  uiion 
tthicli  to  liase  the  contract. 

No  misnndcrstandinfrs  c.-in  arise  when  a 
set  of  otir  plans  and  specifications  are  liel'ore 
the  contractor  and  the  home  luiilder.  show- 
ing the  interior  and  exterior  construction 
of  the  h.iiise  as  ajxreed  upon  in  the  con- 
trai't.  Many  advantaf^cs  may  lie  claimed  for 
the  complete  workiiii:  plans  and  specitica- 
tioiis.  'Ihcy  are  time  savers,  and  therefore 
money  savers.  \\'orkin;;men  will  not  have  to 
wail  for  instructions  when  a  set  of  plans  is  left  on  the  joli.  They  will 
prevent  snistakes  in  nitiiiij:  ImnUcr,  in  phicijij;  door  and  window  frames, 
and  in  many  other  places  when  the  contractor  is  not  on  the  work  and 
the  men  have  received  only  iiartial  or  indetinite  iiistnictio  -s.  They  also 
give  instructions  for  the  working!  of  all  material  to  the  liesi   advantajre. 


Free  Plans  for  Insurance  Adjustment 


You  take  every  prpcaiiiiou  to  luivt-  vmir  I 


loUKe  cnvcnMl  hy  insiirancp 


but  do  you  make  any  provision  for  the  luljiisttneiit  .,f  il 


you  liave  a  fire?     There 


viile  for  ttiis  einha 


le  loss  should 
IS  not  (>ii(>  man  in  ten  llmusand  who  will  pi 


rnissifi);  situ.iiion.     You  cmu  rail  to  mind  inslan^e^ 


in  your  own  locality  where  seillc:iierils  lnv( 


del:. 


insurance  nunp.inies  wauled  some  pronf  which  c ml  I 


d  I 


lecause  tlie 


( 


inch  (•  Kill  not  he  furnished. 

I'hcy  demand  proof  of  loss 

hefor"     paying     insurame 

money,  and  t  hey  are  en  I  il  led 

to  it,       \\c   have  pi  .vided 

for  this  and    have   inaiiitu- 

r.'iled    I  he    follow  inn    plan, 

which  cannot  hut  meet  with 

f.iv(u-  hy  whoever  !)uilds    i 

house  from  our  plans: 

Imiiieili.itely  upon  receipt 

of    information    from    you 

ihal   your  house  ha-     '■,  mi 

dcMrovcd     liv     liic.    •  i.iier 
-—J 

totally  (U-  parli.ally.  we  u  ill 

forward  you.  free  of  cost,  m  duplicate  set  of  plans  and  specificaiions.  and 
inaildition  we  will  fiiriiisli  an  a.lidavil  i,'ivinj:  llie  niimhcr  of  ilic  (i.'.Mi,'ii 
and  <late  when  fiirnislicd.  in  he  used  for  I. le  adjust  mem  of  i  he  insur.im  c 
^^illlout  (ui<"  cent  of  cosi  i:i  you  .and  without  one  p.irlicie  of 
trouhle.  we  keep  a  leconl  of  the  numhcr  of  the  house  desimi  .■mi!  ihe 
<iate  it  was  furnished,  so  tli.n.  in  linie  of  loss,  all  it  will  he  iiccessarv 
for  you  to  do  if  to  drop  us  a  liii'  and  we  will  furiush  the  only  i-ei;al)le 
method  :)f  );el'im;a  spicdy  ati.l  s  ,ii>f.|ct,iry  adiuslmcnl .  This  miv  he  liie 
means  of  savinu'  y.u  liuudreds  ,,f  dillars  l>e,i  li>^  miiCi  time  and  worrv. 

Our  Liberal  Prices 

Many  have  imirveled  at  our  ahility  to 
furiii  h  such  evcellent  and  coMi|ilcle  worki'if; 
phi  ■■  and  specilicalions  at  such  low  prices. 
U  e  do  not  wonder  at  this,  hecaiise  we 
ch.irfie  hul  five  dollars  foi-  ;i  moro  complete 
■set  of  working' |iians  .ami  spei'ificaiioiis  t  han 
you  would  receive  if  ordtu'ed  in  the  rej;ul;'r 
manner,  .-iiid  wiieji  d",iw!i  espci-inlly  for  yr,u, 
at  a  cost  of  from  fifty  to  .«eventy-five  dol- 
lars. On  .account  of  our  large  litisiness 
and  unusual  equipment.  .-iMd  owimr  to  the  fact  that  we  divide  theexjiense 


of  iIh'sc  |plan^  milium  so  iniiiiy,  it  i.-',  imim.miMp  for  us  to  sell  them  at  thCM 
low  prices.  Tin'  iniirKiii  of  jirofit  is  very  el  ■se.  Init  it  eimliles  us  to  sell 
tliousaiiils  of  sets  of  plans,  \vhir!i  save  many  times  tlieir  cost  to  iMith  the 
owner  and  the  contractor  in  erecting  even  the  smallest  ilwellin|{. 


Our  Reliability 

Our  relialiilily  is  Kfvonil  ipiestion.  U'e  have  Ikh'u  in  the  liusiness 
for  many  years,  haviim  (i""'!"'!!  from  a  small  institution  to  our  present 
iarjce  capacity,  pulilishini;  many  hooks  ami  furnishing  plans  and  s|)eci- 
ticalions  for  'iiy  thousands  of  houses  in  all  parts  of  the  I'liited  States, 
Canada,  lluropc.  A'lstralia,  and  South  Africa.  We  presume  this  lK)ok 
may  fall  into  the  hands  of  some  one  who  does  not  know  us;  therefore,  if 
you  ha\e  never  heard  of  us  and  are  not  familiar  with  our  reliahility 
i'ntl  liusiness  methods,  imiuire  of  your  lumlier  dealer  or  hanker.  This 
artii'lc  is  uuneiessary  to  those  who  have  had  previous  dealings  with  us. 
If  you  are  afr.'ti<l  to  send  the  money  direct  to  us,  send  it  with  your  order 
to  The  I'eilcral  Trust  an<l  Savings  Hank,  of  Chicago,  111.  icapital  and 
surplus,  ?i;_'..")(t(».()(MI),  or  to  t!ie  Hiverside  Stale  Hank  of  Hiversiile,  III., 
with  instructions  not  to  turn  it  over  to  us  uidess  they  know  we  are  per- 
fectly reli.ilile  and  will  do  as  we  agree. 

We  have  huilt  tip  our  liusiness  on  these  lines.  We  have  merited 
a  conlinuance  of  patronage  from  our  customers.  We  have  received  the 
lieiielil  of  their  words  of  commendation  to  their  friends.  We  always 
do  exai'ily  as  we  agree. 


Our  Guarantee 

i'erhaps  iliere  are  many  who  feel  that  tliev  are  running  some 
in  ordering  plans  at  a  distance.  We  wish  to  assure  our  customers 
there  is  no  risk  whatever.     If,  upon  receipt  ■ 

of  plans,  you  do  not  liiid  llicm  exactly  as 
we  represent  them,  if  you  lio  no;  fiiul  them 
complete  anil  accurate  in  every  respect ,  if 
vou  do  not  find  them  as  well  prepared  as 
I  hose  furnished  by  any  architect  in  the 
I'nited  Slates,  or  any  that  you  have  ever 
seen,  we  will  refund  your  money  upon  the 
return  of  the  plans  from  you  in  perfect 
condition. 

.Ml  of  our  plans  are  prepared  liy  licensed 
alcliilci  !.■>  >iaudiug  al  tin-  ii<'.i<i  of  tiu-ir  i>r.)- 
fession,  and  the  slamlant  of  their  work  is 
the  very  highest. 


(i 


risk 
that 


/ 


W'f  iiiill.l  mil  .ilTiinl  111  in.ik''  llu-.  yi|:ii:iiilfi"  if  ui'  Hfit-  nut  |>ii>l- 
ll\i>  that  \\i'  VM'ic  riirni'liniu  tlir  ln'«l  |il:iiis  piii  mit  in  iln«  ciiiinlry 
even  I  liinnjh  mir  |in(i'  !■•  nut  iiimic  I  hiiii  iiiM'-»i'\fnlli  tn  uih'-Ii'IiI  h  ul  '  tit 
|nirt'  ii-iiiiliy  rliMriifil 

Lumber  Bill 

Uc  liii  nut  liiiiu-h  M  I  iniiiiT  lull  W-  -i:iic  ilii>  licv  |i:ii'nciil:irly , 
M.'>  siiiMf  |><>ii|ilc  liMM-  :in  1  li>:i  iIkiI  .'I  I  nilici'  liiil  iliiiillil  .'ii  riiin|i:inv  iMi'li 
-ct  uf  |il  III-  .•ml  >|i«M'iticMliiiii>.  Ill  lilt-  lir>t 
|ilari  our  |i1mii-  .•ire  iroltt'ii  \\\>  in  .1  xcrv 
ciiiiii  !rli<Mi>i\<'  11.  iiiin'f.  Ml  liiiil  iiiiy  r:ir|it'ii- 
li'i-  iMii  <M«il\  l;ikc  iitT  tlif  iiinilicl'  lilli  \Mtli- 
iHit  .'iny  iliHiriiliv  \\  <■  K'liJizi'  thai  iIiiti' 
all"  liaiiliv  t«ci  M'll  lulls  (it  I  lie  (until  IV  wluTc 
exactly  tlifsaiiic  kimls  uf  inatfriaU  ;iii"  mmmI, 
ami.  inuiciivcr,  a  liiinlicf  Kill  wliicli  we  iiii>;lit 
t'liriii.-li  wuiilil  not  !«'  apiilicalilf  in  all  sfcliunn 
ul'  the  cuiiiil  i\-.  We  filiiiisli  plan--  ainl  :.jit'(i- 
lic:ii  lull*  t'ur  liiin-cs  wliifli  ai'c  Imill  as  far 
mnlli  as  I'.c  llinlsun  Itay  ami  a-  far  suiitli 
as  llic  I  iiilf  uf  Mrxii'u.  Tlicy  art'  linil;  ijiuii 
I  he  Allaiili"  ami  I'aritii'  coasts,  and  yuii  cin 
alsii  timi  tlicniiii  Aiist ., ilia  ami  Sunt li  Africa. 
Ivicli  cuimlrv  anil  scdiuii  uf  a  cuiintry  lias 
it-    I iiliarilifs    as    to    si/t's   ami  i|nalili<'s, 

I  liiTi'furc  1,  wuiilil  lie  ux'lcss  fur  lis  to  make 
a  li-i  tliat  wuiilil  nut  lie  iiniver-al.  •  >!ir 
liiiuses  ulicn  cunipleteil  may  iuuk  tlies.anie. 
wlietlier    they     are    Imiit     in    <  aiiaila   ur   in 

II  iriila.  Imt  the  same  materials  will  nut  he 
iiseil.  fur  the  reasun  that  the  ciistuiiis  uf  t  he 
peuple  anil  t  lie  clirnatic  ciinditiuiis  will  ilic- 
tate  the  kind  and  aniuuiit  uf  materials  tu  he 
used  in  theii  cunstrucl  i"n. 

Estimated  Cost 

Ir  is  itiipus>ilile  fur  any  uiie  tu  esiim.ate  the  cu>i  uf  a  Imildiii}.'  ami 

lia\e  the  titrnres  liuld  };uud  in  all  -ectiuns  uf  t!i. iiiitry.      'A  e  ilu  nut 

claim  tu  he  ahle  |u  du  it.  The  est  imated  cuM  <>{  the  houses  we  ilhislrate 
i<  l.:!sed  on.  the  mu^t  f:i\ur:r'  Ic  i-undiliuiis  i.'i  all  respects,  ami  dues  nut 
include  pliiinhin;;  and  heating.  We  du  nut  knuw  ymir  lucal  conditions, 
and  should  we  cl.aitn  to  k'luw  the  exact  cu.-l  uf  a  Imildint;  in  your 
localitv,  a  child  would  know  that  mir  stalbtneiit  was  false.    We  advise 


X 


r 


k.  ^^ 


I , 


.■>—■' 


/ 


II 


Mr 


l;li 


'.  r 


r..n.ult«.i..n  with  your  l.M-al  rp«,HmMl.le  nmiermi  a^iil-rH  „„,|  r,.lml.lp 
.■  .Mtn„.|or.,  f.,r  tl...y,  an,l  li.ey  „|,.,„.,  kM„w  y,.„r  Inral  ron.l.lionM  Wo 
U.4.  to  1h.  frank  with  y.,„,  „„.l  th.-rH-r..  ,„„kp  „..  .lut..;,>,.nt  that  «.. 
'•'"not  HulwiMt.iuu..  ill  every  re.|K.rt.     If  ■  uy  ,.hii,  in  tl.i.  I„„,k,  or  in  «nv 

other  lK,ok  we  pul.liMh.  pleas,.,  >ou;  if  the  arran^je-nen,  ,.f  ,1,^  r „s  i". 

MitiHfttelory.  and  if  the  exterior  i,  ,.leasi„«  an,i  at.raeiive.  then  we 
-Make  this  Hain,  -that  it  ran  !«■  l.mlt  as  e:,ea|.ly  as  if  anv  other  Hrehiteel 
cles,«ne.|  ,t,  an.l  we  l«.lieve  ,.hea,K.r.  We  have  stu.lied  eronon.v  in 
.•.n.H.nu-tl.m,  an.l  our  knowle.lae  of  all  the  material  Cat  u-k-s  into"  the 
h..use  .|uah,'ies  us  to  ^jve  you  the  i.est  f„r  y.,ur  inonev.  We  ^ive  you 
:i  P  M  t!iiit  plea.s.-s  you.  ou-  that  is  altrariive.  an.l  one  where  everv 
fool  of  spare  in  utili/e,|  at  ,  he  h-ast  p:,s,il,|e  ,-:,m.  fan  anv  arehite.^t 
•  lo  more,  even  at  seven  I,,  ten  times  the  pri.e  we  rharRe  vou  for  plans' 


Reversing  Plans 


We  re.eive  many  re.p.ests  from  our  patrons  for  plans  ..x:„-,lv  a.vonl- 
ir.K  to  the  .lesions  illustrate.l,  with  the  ,.ne  exreption  of  h-iviuK  lh.-m 

reverse.l  or  face  1  in  l! ,.p,,site  ilire.'ti.ui. 

It  is  im|H.ssil.|e  f,.r  us  t..  make  this  rhantte 
and  draw  new  plans.  e\.ept  at  a  ro>'  „f 
ahoul  eidht  tiriL's  „ur  regular  prices.  We 
see  no  reason  why  our  renular  plans  wi.l  n,.t 
answer  your  purpose.  V.,ur  rariwuiter  can 
fai'P  the  hou.se  e\  icily  as  you  wish  it.  and 
the  jilans  will  w.iri,-  ..ut  as  well  facing  in  one 
•lire.-ii.m  a.s  in  am.ther.  "V  can,  however, 
if  you  wish,  and  .so  in.Mruci  us,  make  y..u  a 
reversed  l.lue  print  ami  furnish  it  a;  .,ur 
>c«ul:ir  jirice.  hut  in  that  ca.se  all  th<  figures 
ami  letlers  will  U-  reverse.l,  and  theref.,re 
liahle  to  cause  as  much  confusi..n  .-is  if  y,„ir 
•arpenter   reverse.l    the    plan   himself  while 

.■oust met iiiK  the  li.,u.se.      We  w.ml.l  a.lvise,  \1. 

iK.wever,  in  all  cases  where  the  |)lan  is  t.)  he 

reversed  and  there  is  the  le..st  .,.,    ahout   the  cmtractor  not  l.ein« 

ahle  to    work    from  the  plans  as  we  have  them,  that   two  .sets  of  Mue 
prints  he  ,.ur,.hase.l.  ..ne  regular  an.l  the  other  rever.se.l,  an.l  in  such 

-•ases  we  will  fi.rmsh  tw..  .sets  of  |.I,.e  prints  a, ne   .se,   of  specifica- 

•■ons  for  .miy  ftfty  ,„.r  cent,  a 1  ,.,  .,ur  re,ml;.r  ...,st .  making  the  .*..  (K) 

plan  cost  .>nly  iT.M). 

Special  Department 

He  have  es-ahlishe.!  a  spe..ial  .lepartment  un.ler  the  supervisi.m  of 
u  license,!  architect,  ..,  luui.lle  all  s,K...ial  plans  which  our  patrons  may 


like  t.i  liiivi-  ilriiwii,  Wf  rt'alur  ih.it  ..flcii  «mi««  H|wiial  or  nnitiiial  iilca 
i.i  wi.-.ln'.l  .■arricl  (.iil,  aii<t  t..  |,iM\i.|.>  for  this  «,■  has.-  mir  ar.lut.Tl.s 
iiticl  iliaiUjlil'iMt'ii.  I'lii'  prirc  \\v  rliuricr  i" 
very  ica^ntialilt'.  Slimilil  ymi  \vi«li  the  wr- 
vircr*  iif  ihiM  ,|,.|.artiui'iit,  ii  vMiiiM  !«•  nc,c»- 
-ary  fnr  y.m  i,.  ,..|i.|  u-  as  full  aiiij  r(iiii|.|rli> 
iiiforti.aliini  as  j...>sil,|,..  aci'iitii|iaiii<M  In  a 
niiiKh  ."kflcli  ilJiiMtatitiK  as  tH'ar  >i»  voii  ran 

yi'nr  iilcas  ati.l   r<-i|i|irt iiis.      Iiiitiiciliali'ly 

il|">M  i<Tfi|ii  of  this  iiilorrnatioii  from  you, 
ui'  will  iiiakr  \oi  a  |iii<f  oii  i  hi-s..  |ilaiis  arni 
-IN-rilicaliotis  rart>iint  out  your  own  idras, 
Mtid  if  our  price  iiiovcs  to  lie  satisfactory .  «<■ 
will  suliiuit  iM-ncil  skffc'li  .sulijfi't  to  your 
rorrccliipiis  ami  adilitiotis  licfori'  |iriMcci|itii: 
In  coMiph-lf  the  |i|,iri>  W  .■  iihim,  lioWfVfr, 
liavi'  an  uii(liM>l;.!iiliiu{  that  we  an-  uiidrr 
I'otitrait  to  ill)  this  work,  for  we  cantioi 
aifi nl  to  do  all  the  |ircliiiiii,ary  Work  without 
soiiir  cuaraiilfcthat  it  Wlli  lie  aircplcd  after 
we  ha\t>  acrcfil  to  make  the  plans  entirely 
.satisfaitory  toy,,..  We  "  II.  however,  make 
/  esiim.'ite  on   the  .-..-i    of    any    >piTi;il    uurk. 

>o  that    you   will   know    e\.iiil\-    \\|i;ii    n    \vill 
rost   you   hefore   we  proi'erd  with  the  pliin^.. 


How  to  Send  Money 

HemitlaiH'es   can   lie    made   l>v    l'o>t    '  iid.  ,•    \|,,ne\    Order,    JApres.s 

Money  Order,  Mank  KraftJ'niled  .<tates  or  (  anadian  l!ill>.     Take  irreal 

care  to  write  yoiu-  addre»    ,il,iinly,  atid   he 

.  jr'  ■■>iil'«'  anil  write  your    nauje  and    addres.s   on 

"^      ,.'      flu'    upper  left-hatid  corner  of  the  envelope. 

Itiadditi      .write  pl.iinly  in  your  letter  voi:- 

naine  ami  address,  the  nan.e  of    \i,ur    city 

county  .and  Slate,  if  you  .are  a    roideni    of 

^        '^ t^~p - :, ,  •« Wfinm».,    the   Cniled  Slalo,  (U-    if    a    re.-ident   of  anv 

jL^-"-^li^_Ui  J  J     "''"■>■    <-ountry.   the    n.ame    of     the     county. 

district    iM-     Province;    also    the    sti-ec     and 

^~    tiiimlier  wlcn  neces.sary.    \\  ■■  receive  a  ^reat 

,'inio:!!;t   o!     !;:.•. ;if--,-    w  l-.ijijj    -.;     .,    iln  jjn.sM  nie    fnr 

-'!<-     "''"  li'ice  on  .iccoutit  of  the  iticiuiiplete  or 
^  itidistinct   writiii;;  of  name  or    aildre.ss,    and 

-\;      oftentimes  the  entire  omission  ijl  hoth. 


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59 


Common-Sense  Stairbuilding  and 
Handrailing 


illustrated 


By  FRED  T.  HODGSON 

ri'^llIS  new  volume  contains  three  (lintinrt  treatiseHon  tlie  siilijert, 
^  each  of  wh'K'h  is  complete  in  itself.  The  system  of  forming  the 
lilies  fur  ohtaininc  the  viirioiis  curves,  wreaths,  ramps  and  face 
mouhls  for  handrails  are  the  simplest  in  use  and  those  employed  by  the 
most  successful  haiidrailers.  Mr.  Ilodftson  has  placed  this'  unusually 
intricate  sul>ject  hefore  his  readers  in  a  very  plain  and  easilv  understooil 
manner,  and  any  workman  haviii):  a  fair  knowledge  of  "lines"  and  who 
can  construct  an  ordimny  straight  stairway  can  readily  grasp  the  whole 
system  of  '•handrailing"  after  a  sin;ill  st\idy  of  this  W'ork. 

The  liuilding  of  stairs  and  |>roi)e;ly  making  and  ])lacing  over  them  a 
graceful  handrail  and  suitable  balusters  and  newel  |)osts  is  one  of  the 
greatest  achievements  of  the  joiner's  art  and  skill,  yet  it  is  an  art  that 
is  the  least  understood  of  ;my  of  the  constructive  processes  the  cari)enter 
or  joiner  is  called  upon  to  accomplish.  In  but  very  few  of  the  plans 
jiiade  by  an  architect  are  the  stairs  pro|)erly  laid  down  or  divided  off; 
indeed,  tnost  of  the  stairs  as  laid  out  and  piatuied  liy  the  architect  are 
impo.ssible  ones,  owing  to  the  fact  that  the  circumsiances  that  govern 
the  formation  of  the  rail  are  either  not  understood  or  not  noticed  by 
the  designer,  and  the  expert  handrailer  often  finds  it  difhcult  to  con", 
foriii  the  stairs  and  rail  to  the  jilan.  (lenerally,however, he  gets  so  close 
to  it  that  the  character  of  the  design  is  sehlom  changed. 

The  stairs  are  the  great  feature  of  a  building  as  they  are  the  first 
object  that  meets  the  visitor  and  claims  his  attention, and  it  is  es.scniial, 
therefore,  that  tlie  stair  and  its  adjuncts  should  have  a  neat  and  graceful 
appearance,  and  this  can  oidy  be  accomplished  by  having  the  rail  jirop- 
;  rly  made  and  set  up. 

This  little  book  gives  such  instructions  in  the  art  of  handrailing  as 
will  enable  the  young  workman  to  l>uild  a  rail  .so  that  it  will  a.s.-ume  a 
handsome  appe:irMiicc  wlien  .set  in  pl;ice.  There  are  eleven  distinct 
styles  of  stairs  shown,  but  the  same  principle  that  go\erns  the  making 
of  the  simplest  rail,  governs  the  construction  of  the  most  difficult,  .so, 
once  having  mastered  I  he  simple  problems  in  this  system,  progress  iti 
(lie  art  will  become  easy,  and  a  little  study  anil  -ractice  will  enable  the 
Workman  to  construct  a  rail  for  the  most  tortui.iis  stairway. 

The  book  is  copiously  illustrated  with  nearly  one  hundred  working 
di;ii;rams  together  with  full  descriptive  text. 

Price,  $1.00.   Address  all  orders  to 

THE  RADF^flD  ARCHITECTURAL  CO. 

Chicago  Office:  190  W.  22d  St.      RIVERSIDE,  ILL.,  U.S.A. 
New  Yorii  Office:  822-824  Broadway 

60 


PRACTICAL  USES  OF  THE 

STEEL 
SQUARE 

AMODKHX  TIJKATlSi;  ).y  1  n-<l  T.  Ilodcson.  An  pxhaiisilvp 
work  incliidiii^  a  liricf  lii.-torv  of  tlip  Scpiarc;  a  (Ifsrriplioti  of 
many  of  the  S^i  lacs  lliat  art-  now.  imd  li:ivt'  liccii  in  the  niaikel. 
inrludinK  w)Mio  very  inncniows  devices  for  layinj;  out  lirvels  for  Uafters, 
lirace.s  and  oilier  iru'lined  work;  also  cliapters  on  I  he  Si|iiare  as  a  oal- 
eidating  [^iiicliine.sliowin;;  how  to  measure Sohds,  Surfaces  and  Distances 
— very  useful  to  builders  and  esti;na.tors.  ('Iia|iters  on  roofiii;;  and 
how  to  form  tliem  liy  the  aid  of  the  S(|uare:  ((cta^con.  liexajion,  Hi]), 
and  other  Hoofs  are  shown  and  explainecl,  and  the  manner  of  gettin;! 
the  rafters  and  jacks  ^;iven.  ('ha|iterson  lieavvtindK-r  fraiiiinj;. showing 
how  the  S<iuare  is  used  for  layinjl  out  Mortises.  Tenons,  .'shoulders. 
Inclined  Work.  An;:le  Corners  anil  .similar  work. 

The  work  abounds  wiili  hundreds  of  fine  illustrations  and  explana- 
tory di'uirams.  which  will  prove  a  [lerfect  mine  of  instruction  for  the 
mechanic,  youn);  or  old. 

Two  large  volumes,  boimd  in  fine  cloth,  printed  on  a  superior  ([iiality 
of  paper  from  new  larije  type. 

Price,  2  Volumes,  Cloth  Bindinji:,  $2.00 

Publishers'  Note.  We  wish  to  state  this  work  is  entirely 
new  and  must  not  be  mistaken  loi'  Mr.  Hodgson's  former  works  on  the 
".Steel  .S(|.iaie.  "  wliii  1  were  published  some  twenly  yciirs  af;o.  He  sure 
and  ^fM  "I'ractical  I'ses  of  (he  Steel  S.|  i.are,"  by  lie.!  T.  Hodgson. 
Address  all  orders  to 

The  Radford  Architectural  Co. 

RIVERSIDE,  ILL,,  U.  S.  A. 

ChicaKO  Office:     190    W.  aid  Street 
New  York  Office:  822-824  Broadway 


61 


BmumBa 


The  Radford 

American  Homes 


100  House  Plans 

Illustrated 


This  is  :i  new  book  of  low  and  niedinni  ])riced 
lionse  plans. 

It  contains  all  of  the  latest  styles 
of  architecture. 

This  book  is  hand.somely  bo'uul  in  Knglish 

cloth,  cover  embossed  in  three  colors, 

gilt  top. 

256  pages. 


Price  :    $1.00,  postage  paid 


The  Radford  Architectural  Co. 


Chicafio 


Riverside,  III..  U.S.  A.  New  York 


The  Radford 

Ideal  Horn 


100  House  Plans 

Illustrated 


This  is  tlic  book  of  house  plans  whicli  h:is 
met  ^  ith  such  wonderful  success. 

It  contains   loo  low  and  medium  priced 
lu)use  designs. 

Handsomely  bound  in  Engli.sli  cloth,  covtr 
embossed   in  colors. 

Si/e,  S    :    1 1    inches. 


Price:    $1.00,  postage  paid 


The  Radford  Architectural  Co. 

Chicago  Riverside,  III.,  U.S.A.  New  York 


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